bluuebunny/crossref_metadata_2025 huggingface dataset:
The Space of Dirichlet-Finite Solutions of the Equation Δu = Pu on a Riemann Surface
Authors: Nakai Mitsuru
Published: July 2016

Let R be an open Riemann surface. By a density P on R we mean a non-negative and continuously differentiable functions P(z) of local parameters z = x + iy such that the expression P(z)dxdy is invariant under the change of local parameters z. In this paper we always assume that P≢0 unless the contrary is explicitly mentioned. We consider an elliptic partial differential equation

which is invariantly defined on R.
Abstract Evolution Equations of Parabolic Type in Banach and Hilbert Spaces
Authors: Kato Tosio
Published: July 2016

The object of the present paper is to prove some theorems concerning the existence and the uniqueness of the solution of the initial value problem for the evolution equation

(E).
The Hessian map in the invariant theory of reflection groups
Authors: Orlik Peter , Solomon Louis
Published: July 2016

Let V be a complex vector space of dimension l. Let S be the C-algebra of polynomial functions on V. Let Ders be the S-module of derivations of S and let Ωs = Homs (Ders, S) be the dual S-module of differential 1-forms. Let {ei} be a basis for V and let {xi} be the dual basis for V. Then {Di = ∂/∂xi and {dxi} are bases for Ders and Ωs as S-modules. If f ∈ S, define a map Hess (f): Ders → Ωs by

Then Hess (f) is an S-module homomorphism which does not depend on the choice of basis for V.
Categories of multiplicative functors and Weil’s infinitely near points
Authors: Luciano O. O.
Published: July 2016

At the early fifties A. Weil introduced [3] and algebraic approach to the theory of infinitesimal prolongations of smooth manifolds motivated by the theory of jets developed by Ch. Ehresmann on one side and also by the return to Fermat’s methods on the infinitesimal calculus of first order, that makes use of nilpotent infinitesimals.
Generalized Ono invariant and Rabinovitch’s theorem for real quadratic fields
Authors: Sasaki Ryuji
Published: July 2016

Letdbe a square-free integer. Let

and {1,ω} forms aZ-basis for the ring of integers of the quadratic fieldWe denote byΔandhdthe discriminant and the class number ofrespectively.
Dedekind sums and quadratic residue symbols
Authors: Ito Hiroshi
Published: July 2016

In this paper we first prove a simple relation between sums of a certain type and quadratic residue symbols. Then we apply this to Dedekind sums introduced by Sczech [5]. In particular one of his conjectures in [6] will be proved.
A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups
Authors: Obata Nobuaki
Published: July 2016

P. Lévy introduced, in his celebrated books [21] and [22], an infinite dimensional Laplacian called the Lévy Laplacian in connection with a number of interesting topics in variational calculus. One of the most significant features of the Lévy Laplacian is observed when it acts on the singular part of the second functional derivatives. For this reason the Lévy Laplacian has become important also in white noise analysis initiated by T. Hida [12]. On the other hand, as was pointed out by H. Yoshizawa [29], infinite dimensional rotation groups are profoundly concerned with the structure of white noise, and therefore, play essential roles in certain problems of stochastic calculus. Motivated by these works, we aim at developing harmonic analysis on infinite dimensional spaces by means of the Lévy Laplacian and infinite dimensional rotation groups.
A calculus approach to hyperfunctions III
Authors: Matsuzawa Tadato
Published: July 2016

In the previous papers, [18] and [19], we have given some basis of a calculus approach to hyperfunctions. We have taken hyperfunctions with the compact support as initial values of the solutions of the heat equation. More precisely, letA′[K]be the space of analytic functionals supported by a compact subsetKofRnand letE(x, t)be then-dimensional heat kernel given by

.
Birational automorphism groups and differential equations
Authors: Umemura Hiroshi
Published: July 2016

Painlevé studied the differential equations y″ = R(y′ y, x) without moving critical point, where R is a rational function of y′ y, x. Most of them are integrated by the so far known functions. There are 6 equations called Painlevé’s equations which seem to be irreducible or seem to define new transcendental functions. The simplest one among them is y″ = 6y2 + x. Painlevé declared on Comptes Rendus in 1902-03 that y″ = 6y2 + x is irreducible. It seems that R. Liouville pointed out an error in his argument. In fact there are discussions on this subject between Painlevé and Liouville on Comptes Rendus in 1902-03. In 1915 J. Drach published a new proof of the irreducibility of the differential equation y″ = 6y2 + x. The both proofs depend on the differential Galois theory developed by Drach. But the differential Galois theory of Drach contains errors and gaps and it is not easy to understand their proofs. One of our contemporaries writes in his book: the differential equation y″ = 6y2 + x seems to be irreducible dans un sens que on ne peut pas songer à préciser. This opinion illustrates well the general attitude of the nowadays mathematicians toward the irreducibility of the differential equation y″ = 6y2 + x. Therefore the irreducibility of the differential equation y″ = 6y2 + x remains to be proved. We consider that to give a rigorous proof of the irreducibility of the differential equation y″ = 6y2 + x is one of the most important problem in the theory of differential equations.
Bernsteins theorem for completely excessive measures
Authors: Saad Hedi Ben , Janßen Klaus
Published: July 2016

Bernstein’s theorem states that the following properties are equivalent for a function ψ:]0, ∞ [→ R (which then is called completely monotone):

moreover, the measure σ in iii) is uniquely determined.
Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note
Authors: Sato Mikio , Shintani Takuro
Published: July 2016

The purpose of this paper is to introducea-functions andb-functions of prehomogeneous vector spaces in the original way of M. Sato and give a proof of the structure theorem of them. All the results were obtained by M. Sato when he constructed the theory of prehomogeneous vector spaces in 60’s. However he did not write a paper on his outcomes at that time. His theory was distributed through his lectures and informal seminars. Only small number of people could know it. The only publication left for us is a mimeographed note of his lecture [Sa-Sh1] written by T. Shintani in Japanese.
On the length of the powers of systems of parameters in local ring
Authors: Tu Cuong Nguyen
Published: July 2016

Throughout this note, A denotes a commutative local Noetherian ring with maximal ideal m and M a finitely generated A-module with dim (M) = d. Let x1, …, xd be a system of parameters (s.o.p. for short) for M and I the ideal of A generated by x1, …, xd.
On defect relations of moving hyperplanes
Authors: Shirosaki Manabu
Published: July 2016

The defect relation gives the best-possible estimate, where f is a linearly non-degenerate holomorphic curve in Pn(C) and H1, …, Hq are hyperplanes in Pn(C) which are in general position. However, the case of moving hyperplanes has ever got only n(n + 1) instead of n + 1 (Stoll [4]) and it has not yet been known whether this bound is best-possible or not. In this paper we shall give some particular cases which have the bound n + 1.
Holomorphic mapping into algebraic varieties of general type, II
Authors: Hu Peichu
Published: July 2016

This announcement is a continuation of Hu [3]. Our results improve Theorem 1 of [3], but the latter is needed in the proof of the former.

Let f: M → N be a holomorphic mapping from a connected complex manifold M of dimension m to a projective algebraic manifold N of dimension n.
Young diagrammatic methods in non-commutative invariant theory
Authors: Teranishi Yasuo
Published: July 2016

In this paper we will study some aspects of non-commutative invariant theory. Let V be a finite-dimensional vector space over a field K of characteristic zero and let

K[V] = K⊕V⊕S2(V)⊕…, and

K′V› = K⊕V⊕⊕2(V)⊕⊕3V⊕&

be respectively the symmetric algebra and the tensor algebra over V. Let G be a subgroup of GL(V). Then G acts on K[V] and K′V›. Much of this paper is devoted to the study of the (non-commutative) invariant ring K′V›G of G acting on K′V›.

In the first part of this paper, we shall study the invariant ring in the following situation.
Explicit descriptions of trace rings of generic 2 by 2 matrices
Authors: Teranishi Yasuo
Published: July 2016

Let K be a field of characteristic zero and let

be m generic n by n matrices over K. That is, xij(k) are independent commuting indeterminates over K. The K-subalgebra generated by X1…, Xm is called a ring of n by n generic matrices and is denoted by R(n, m).
Notes on energy for space-time processes over Lévy processes
Authors: Kanda Mamoru
Published: July 2016

LetX=(Xt, 0 ≤t< ∞) be a Lévy process on the Euclidean spaceRd, that is, a process onRdwith stationary independent increments which has right continuous paths with left limits. We denote byPxthe probability measure such thatPX(X0= x)= 1 and byExthe expectation relative toPx. The process is characterized by the exponentΨthrough

.
Sur les fonctions périodiques de plusieurs variables
Authors: Abe Yukitaka
Published: July 2016

Les fonctions périodiques d’une seule variable ont été étudiées depuis longtemps. On sait que toute fonction méromorphe de n variables 2n fois périodiques peut s’écrire comme quotient de deux fonctions thêta. Ceci est a l’origine de l’essor des fonctions thêta. Au contraire, l’étude des fonctions périodiques de n variables r fois périodiques (r < 2n) a pris du retard. Il nous semble que P. Cousin ([4] et [5]) a étudié ces fonctions pour la première fois.
The generalized divisor problem and the Riemann hypothesis
Authors: Nakaya Hideki
Published: July 2016

Let dz(n) be a multiplicative function defined by

where s = σ + it, z is a. complex number, and ζ(s) is the Riemann zeta function. Here ζz(s) = exp(z log ζ(s)) and let log ζ(s) take real values for real s > 1. We note that if z is a natural number dz(n) coincides with the divisor function appearing in the Dirichlet-Piltz divisor problem, and d-1(n) with the Möbious function.
Integral-geometric construction of self-similar stable processes
Authors: Takenaka Shigeo
Published: July 2016

Recently, fractional Brownian motions are widely used to describe complex phenomena in several fields of natural science. In the terminology of probability theory the fractional Brownian motion is a Gaussian process{X(t) :tє R} with stationary increments which has a self-similar property, that is, there exists a constantH(for the Brownian motionH= 1/2, in general 0 <H< 1 for Gaussian processes) called the exponent of self-similarity of the process, such that, for anyc> 0, two processesare subject to the same law (see [10]).
Optimal control for stochastic partial differential equations and viscosity solutions of Bellman equations
Authors: Nisio Makiko
Published: July 2016

Recently M. G. Crandall and P. L. Lions developed the viscosity theory on nonlinear equations in infinite dimensions and optimal control in Hilbert spaces, in two series of papers, [1], [4].
Distributions of stable random fields of Chentsov type
Authors: Sato Yumiko
Published: July 2016

In this paper we discuss the determinism of distributions of some stable random fields which are constructed through integral-geometric method. The determinism depends on the dimension of the parameter space Rd.
Ito’s formula and Levy’s Laplacian II
Authors: Saito Kimiaki
Published: July 2016

The white noise calculus was initiated by T. Hida in 1970 in his Princeton University Mathematical Notes [3]. Recent development of the theory shows that the Laplacian plays an essential role in the analysis in question. Indeed, several kinds of Laplacians should be introduced depending on the choice of the class of white noise functionals to be analysed, as can be seen in [4], [13], [18] and so forth. Among others, we should like to emphasize the importance of the infinite dimensional Laplace-Beltrami operator, Volterra’s Laplacian and Lévy’s Laplacian (See [13], [18] and [20]).
Ideals of bounded holomorphic functions on simple n-sheeted discs
Authors: Hara Masaru
Published: July 2016

As usual we denote by H∞(K) the Banach algebra of bounded holomorphic functions on a Riemann surface R equipped with the supremum norm ‖·‖ Consider the ideal I(f1 … fm) of H∞(R) generated by functions f1 …fm in H∞(R). If a function g in H∞(R) belongs to I(f1 … fm or equivalently, if there exist m functions h1 …, hm in H∞(R) with

on R, then common zero points of f1, ... fm are also zero points of g in the following strong sense:

on R for a positive constant δ > 0. The generalized corona problem asks whether the converse is valid or not. In the case g ≡ 1 on R the problem is referred to simply as the corona problem.
Rees algebras of non-singular equimultiple prime ideals
Authors: Herrman, M. , Ribbe J. , Trung N.V.
Published: July 2016

In a recent paper [HI2] the first named author and S. Ikeda have investigated Gorenstein properties under blowing up of height two equimultiple ideals from the arithmetical point of view. The problem is to what extent does the Gorenstein property of the Rees algebra R(a) = of an equimultiple ideal a of a local ring (A, m) describe the structure of A and a. One result is that if A is a generalized Cohen-Mac aulay ring (i.e. a ring of finite local cohomology) with dim (A) ⊇ 4 and if there is an height two equimultiple prime ideal p such that R(p) is Gorenstein, then A is Gorenstein and p is generated by a regular sequence (see [HI2], Theorem 2.6). That has led to the question whether this result is still valid for dim (∧) = 3. ∧ partial answer was given in [HI2], Proposition 2.10, where “equimultiplicity” was replaced by the stronger condition “p/p2 is flat over A/p”
The stationary phase method with an estimate of the remainder term on a space of large dimension
Authors: Fujiwara Daisuke
Published: July 2016

In discussing convergence of Feynman path integrals [2], we need a stationary phase method of oscillatory integrals over a space of large dimension. More precisely, we have to know how the remainder term behaves when the dimension of the space goes to ∞ (cf. [2], [3] and [5]). The aim of the present note is to give answer to this question under rather mild assumptions. Application to the Feynman path integrals is discussed in [3] and [5].
The growth of the bergman kernel on pseudoconvex domains of homogeneous finite diagonal type
Authors: Herbort Gregor
Published: July 2016

In this article we continue the investigations on invariant metrics on a certain class of weakly pseudoconvex domains which we began in [H 1]. While in that paper the differential metrics of Caratheodory and Kobayashi were estimated precisely, the present paper contains a sharp estimate of the singularity of the Bergman kernel and metric on domains belonging to that class.
Infinite dimensional cycles associated to operators
Authors: Morimoto Hiroshi
Published: July 2016

A family of operators defined on infinite dimensional spaces gives rise to interesting cycles (or subvarieties) of infinite dimension which represent a topological or non-topological feature of operator families. In this paper we will give a general theory of these cycles, and give some estimates among them. We will apply this theory, in the final section, to cycles derived from Dirac operators.
On the L2 cohomology of complex spaces II
Authors: Ohsawa Takeo
Published: July 2016

This is a continuation of the author’s previous work [0-6], in which we have settled a conjecture of Cheeger-Goresky-MacPherson [C-G-M] by proving that the L2 cohomology group of a compact (reduced) complex space is canonically isomorphic to its (middle) intersection cohomology group. Our aim here is, in addition to that result, to extend further the classical L2 harmonic theory to complex spaces with arbitrary singularities by establishing the following.
Unitary representations of unipotent groups associated with theta series
Authors: Morikawa Hisasi
Published: July 2016

1. Unipotent group of real (g + 2) × (g + 2) -matrices

may be regarded as a split extension of Ng (R) by Heisenberg group of real (g + 2) × (g + 2)-matrices
Anisotropic random walks on free products of cyclic groups, irreducible representations and idempotents of C*reg(G)
Authors: Kuhn Gabriella
Published: July 2016

Let be the free product of q + 1 copies of Zn+1 and let denote its Cayley graph (with respect to aj, 1 ≤ j ≤ q + 1). We may think of G as a group acting on the “homogeneous space” , This point of view is inspired by the case of SL2(R) acting on the hyperbolic disk and is developed in [FT-P] [I-P] [FT-S] [S] (but see also [C]).

Since G is a group we may investigate some classical topics: the full (reductive) C* algebra, its dual space, the regular Von Neumann algebra and so on. See [B] [P] [L] [V] and also [H]. These approaches give results pointing up the analogy between harmonic analysis on these groups and harmonic analysis on more classical objects.
Fourier-Eisenstein transform and plancherel formula for rational binary quadratic forms
Authors: Hironaka Yumiko , Sato Fumihiro
Published: July 2016

Let X be the space of nondegenerate rational symmetric matrices of size 2 and put

The group G acts on X by

We are interested in the space (Γ\X) of Γ-invariant C-valued functions on X and its subspace &(Γ\X) of functions whose supports consist of a finite number of Γ-orbits. The Hecke algebra ℋ(G, Γ) of G with respect to Γ acts naturally on these spaces.
On vector bundles on algebraic surfaces and 0-cycles
Authors: Ballico E.
Published: July 2016

Let X be an algebraic complex projective surface equipped with the euclidean topology and E a rank 2 topological vector bundle on X. It is a classical theorem of Wu ([Wu]) that E is uniquely determined by its topological Chern classes . Viceversa, again a classical theorem of Wu ([Wu]) states that every pair (a, b) ∈ (H (X, Z), Z) arises as topological Chern classes of a rank 2 topological vector bundle. For these results the existence of an algebraic structure on X was not important; for instance it would have been sufficient to have on X a holomorphic structure. In [Sch] it was proved that for algebraic X any such topological vector bundle on X has a holomorphic structure (or, equivalently by GAGA an algebraic structure) if its determinant line bundle has a holomorphic structure. It came as a surprise when Elencwajg and Forster ([EF]) showed that sometimes this was not true if we do not assume that X has an algebraic structure but only a holomorphic one (even for some two dimensional tori (see also [BL], [BF], or [T])).
Asymptotic dependence of moving average type self-similar stable random Fields
Authors: Kokoszka Piotr S. , Taqqu Murad S.
Published: July 2016

As non-Gaussian stable stochastic processes have infinite second moments, one cannot use the covariance function to describe their dependence structure.
On L-functions associated with the vector space of binary quadratic forms
Authors: Saito Hiroshi
Published: July 2016

The purpose of this paper is to prove functional equations of L-functions associated with the vector space of binary quadratic forms and determine their poles and residues. For a commutative ring K, let V(K) be the set of all symmetric matrices of degree 2 with coefficients in K. In V(C), we consider the inner product

where for .
Differential games for stochastic partial differential equations
Authors: Fleming W.H. , Nisio M.
Published: July 2016

In this paper we are concerned with zero-sum two-player finite horizon games for stochastic partial differential equations (SPDE in short). The main aim is to formulate the principle of dynamic programming for the upper (or lower) value function and investigate the relationship between upper (or lower) value function and viscocity solution of min-max (or max-min) equation on Hilbert space.
P-harmonic dimensions on ends
Authors: Kawamura Michihiko , Segawa Shigeo
Published: July 2016

Consider an end Ω in the sense of Heins (cf. Heins [3]): Ω is a relatively non-compact subregion of an open Riemann surface such that the relative boundary ∂Ω consists of finitely many analytic Jordan closed curves, there exist no non-constant bounded harmonic functions with vanishing boundary values on ∂Ω and Ω has a single ideal boundary component. A density P = P(z)dxdy (z = x + iy) is a 2-form on Ω∩∂Ω with nonnegative locally Holder continuous coefficient P(z).
Depth formulas for certain graded rings associated to an ideal
Authors: Huckaba Sam , Marley Thomas
Published: July 2016

In this paper, we investigate the relationship between the depths of the Rees algebra R[It] and the associated graded ring grI(R) of an ideal I in a local ring (R, m) of dimension d > 0. Here

and

.
Explicit formulas for local factors: Addenda and errata
Authors: Feit Paul
Published: July 2016

In [3], the author studied certain local integrals derived from Fourier coefficient computations on Eisenstein series. Members of a family of Dirichlet series were characterized as a product of an explicit term with a mysterious polynomial factor. In a recent letter to the author, Professor Shoyu Nagaoka asked specific questions concerning the polynomial factor. Several of these questions can be answered by the techniques in [3]. In Part I of that paper, the relevant term is described precisely; however, in Part II, the term is described as a mysterious, albeit finite, sum. The present paper complete [3] by recording what little is known of that sum.
Decomposition problem of probability measures related to monotone regularly varying functions
Authors: Shimura Takaaki
Published: July 2016

This paper deals with a decomposition problem for some classes of distributions. Let D be a given class of distribution on R1, which we are interested in. After showing that the class D is closed under convolution, our purpose is to give an answer to the inverse problem: if the convolution of two distributions μ1 and (μ2 belongs to D, then do μ1 and μ2 belong to D?
Thick sets and quasisymmetric maps
Authors: Väisälä Jussi , Vuorinen Matti , Wallin Hans
Published: July 2016

1.1. Thickness. Let E be a real inner product space. For a finite sequence of points a0, . . . ,ak in E we let a0. . . ,ak denote the convex hull of the set {a0, . . . , ak}. If these points are affinely independent, the set Δ = a0. . .ak is a k-simplex with vertices a0. . . ,ak. It has a well-defined k-volume written as mk(Δ) or briefly as m(Δ). We are interested in sets A ⊂ E which are “nowhere too flat in dimension k”. More precisely, suppose that A ⊂ E, q > 0 and that k: is a positive integer. We let denote the closed ball with center x and radius r. We say that A is (q, k)-thick if for each x ∈ A and r> 0 such that A\ ≠ there is a k-simplex Δ with vertices in A ∩ such that mk(Δ) ≥ qr.
Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space
Authors: Miyake Masatake , Yoshino Masafumi
Published: July 2016

In the study of ordinary differential equations, Malgrange ([Ma]) and Ramis ([R1], [R2]) established index theorem in (formal) Gevrey spaces, and the notion of irregularity was nicely defined for the study of irregular points. In their studies, a Newton polygon has a great advantage to describe and understand the results in visual form. From this point of view, Miyake ([M2], [M3], [MH]) studied linear partial differential operators on (formal) Gevrey spaces and proved analogous results, and showed the validity of Newton polygon in the study of partial differential equations (see also [Yn]).
The Dirichlet problem at infinity on Hadamard manifolds
Authors: Kumura Hironori
Published: July 2016

Let M be an n-dimensional Hadamard manifold, that is, a complete simply connected C∞ Riemannian manifold with nonpositive sectional curvatures. Making use of geodesic rays, Eberlein and O’Neill [11] constructed a compactification = MS(∞) of M which gives a homeomorphism of (M, S(∞)) with the Euclidean pair (Bn, Sn-1). In this paper we shall study the asymptotic Dirichlet problem for the Laplace-Beltrami operator, which is stated as follows:
Boundary behaviour of extremal plurisubharmonic functions
Authors: Einstein-Matthews Stanley M.
Published: July 2016

In [Mo.l], S. Momm studied the boundary behaviour of extremal plurisubharmonic functions by using the pluricomplex Green function gΩ of a bounded convex domain Ω in Cn to exhaust the domain by a family of sublevel sets. Let Ω be a bounded convex domain in Cn containing the origin in its interior. The pluricomplex green function of Ω with a pole
is defined by

(1.1)
Intersection theory for twisted cohomologies and twisted Riemann’s period relations I
Authors: Cho Koji , Matsumoto Keiji
Published: July 2016

The beta function B(α, β) is defined by the following integral

where arg , and the gamma function Γ(β) by

where arg .
Riesz capacity and regular boundary points for the parabolic operator of order α
Authors: Nishio Masaharu
Published: July 2016

Let Rn+1 = Rn × R be the (n + 1)-dimensional Euclidean space with n ≥ 1. We denote by X = (x, t) a point in Rn+1 with x ∈ Rn and t ∈ R. Consider the parabolic operator on Rn+1:

where 0 < a ≤ 1 and Δ denotes the Laplacian on Rn.
Surfaces associées au plongement canonique des courbes
Authors: D’Almeida Jean
Published: July 2016

Soit C une courbe canonique de genre g ≥ 4. Le théorème de Enriques-Babbage [ACGH] affirme que l’idéal de C est engendré par (g − 2) (g − 3)/2 hypersurfaces quadriques sauf si C est trigonale ou isomorphe à une quintique plane. Si C est trigonale, elle est tracée sur une surface réglée rationnelle normale dont les génératrices découpent la série trigonale. Si C est isomorphe à une quintique plane lisse, elle est tracée sur une surface de Veronése.
A construction of peak functions on locally convex domains in Cn
Authors: Cro Sanghyun
Published: July 2016

Let Ω be a smoothly bounded pseudoconvex domain in Cn and let A(Ω) denote the functions holomorphic on Ω and continuous on . A point p ∈ bΩ is a peak point if there is a function f ∈ A(Ω) such that f (p) = 1, and | f(z) | < 1 for z ∉ Ω − {p}.
Multidimensional process of Ornstein-Uhlenbeck type with nondiagonalizable matrix in linear drift terms
Authors: Sato Ken-Iti , Watanabe Toshiro , Yamamuro Kouji , Yamazato Makoto
Published: July 2016

Let Rd be the d-dimensional Euclidean space where each point is expressed by a column vector. Let | x | and ‹x, y› denote the norm and the inner product in Rd. Let Q = (Qjk) be a real d × d-matrix of which all eigenvalues have positive real parts. Let X be a process of Ornstein-Uhlenbeck type (OU type process) on Rd associated with a Levy process {Z: t ≥ 0} and the matrix Q. Main purpose of this paper is to give a recurrence-transience criterion for the process X when Q is a Jordan cell matrix and to compare it with the case when Q is diagonalizable. Here by a Levy process we mean a stochastically continuous process with stationary independent increments, starting at 0.
Algebraic Barth-Lefschetz theorems
Authors: Bădescu Lucian
Published: July 2016

We shall work over a fixed algebraically closed field k of arbitrary characteristic. By an algebraic variety over k we shall mean a reduced algebraic scheme over k. Fix a positive integer n and e = (e0, el,…, en) a system of n + 1 weights (i.e. n + 1 positive integers e0, el,…, en). If k[T0, Tl,…, Tn] is the polynomial k-algebra in n + 1 variables, graded by the conditions deg(Ti) = ei i = 0, 1,…, n, denote by Pn(e) = Proj(k[T0, T1,…, Tn]) the n-dimensional weighted projective space over k of weights e. We refer the reader to [3] for the basic properties of weighted projective spaces.
Limit theorems related to a class of operator-self-similar processes
Authors: Maejima Makoto
Published: July 2016

An Rd-valued (d ≥ 1) stochastic process X = {X(t)}t≥0 is said to be operator-self-similar if there exists a linear operator D on Rd such that for each c > 0

where means the equality for all finite-dimensional distributions and
Finite arithmetic subgroups of GLn, IV
Authors: Kitaoka Yoshiyuki , Suzuki Hiroshi
Published: July 2016

In this paper, we improve a result of the third paper of this series, that is we show

THEOREM. Let K be a nilpotent extension of the rational number field Q with Galois group Γ, and G a Γ- stable finite subgroup of GLn(0K). Then G is of A-type.
On a Ring Isomorphism Induced by Quasiconformal Mappings
Authors: Nakai Mitsuru
Published: July 2016

The purpose of this paper is to study the relationship between a certain isomorphism of some rings of functions on Riemann surfaces and a quasi-conformal mapping.

It is well known that two compact Hausdorff spaces are topologically equivalent if and only if their rings of continuous functions are isomorphic. We shall establish an analougous result concerning a function ring on a Riemann surface and the quasi-conformal equivalence.
On Unramified Separable Abelian p-Extensions of Function Fields I
Authors: Morikawa Hisasi
Published: July 2016

Let k be an algebraically closed field of characteristic p>0. Let K/k be a function field of one variable and L/K be an unramified separable abelian extension of degree pr over K. The galois automorphisms ε1, …, εpr of L/K are naturally extended to automorphisms η(ε1), … , η(εpr) of the jacobian variety JL of L/k. If we take a svstem of p-adic coordinates on JL, we get a representation {Mp(η(εv))} of the galois group G(L/K) of L/K over p-adic integers.
Newforms of half-integral weight
Authors: Shemanske Thomas R.
Published: July 2016

Two very different definitions of a newform of half-integral weight are present and continued to be developed in the literature. The first definition originated with Serre and Stark for forms of weight 1/2 [5], and is analogous to the definition of newform for integral weight forms, which uses forms of lower level and shifts of such forms to characterize the notion of old-forms. The second definition originated with Kohnen for half-integral weight forms of squarefree level [1], who used forms of lower level and their image under the Um2 operator to define the notion of oldforms. The choice of the Um2 operator over the shift operator Bd seems a propitious one, since the U operator commutes with the action of the Shimura lift, while the shift operator B does not. More to the point, Kohnen was able to develop a newform theory on a distinguished subspace of the full space of cusp forms (now referred to as the Kohnen subspace), and obtained a multiplicity-one result (with respect to Hecke eigenvalues) for half-integral weight newforms in this subspace. Even nicer, the multiplicity-one result was established by showing that there is a one-to-one correspondence between newforms of level AN in the subspace and the newforms of integral weight of level N.
Galois theory of aigebraic and differential equations
Authors: Umemura Hiroshi
Published: July 2016

This paper will be the first part of our works on differential Galois theory which we plan to write. Our goal is to establish a Galois Theory of ordinary differential equations. The theory is infinite dimensional by nature and has a long history. The pioneer of this field is S. Lie who tried to apply the idea of Abel and Galois to differential equations. Picard [P] realized Galois Theory of linear ordinary differential equations, which is called nowadays Picard-Vessiot Theory. Picard-Vessiot Theory is finite dimensional and the Galois group is a linear algebraic group. The first attempt of Galois theory of a general ordinary differential equations which is infinite dimensional, is done by the thesis of Drach [D]. He replaced an ordinary differential equation by a linear partial differential equation satisfied by the first integrals and looked for a Galois Theory of linear partial differential equations. It is widely admitted that the work of Drach is full of imcomplete definitions and gaps in proofs. In fact in a few months after Drach had got his degree, Vessiot was aware of the defects of Drach’s thesis. Vessiot took the matter serious and devoted all his life to make the Drach theory complete. Vessiot got the grand prix of the academy of Paris in Mathematics in 1903 by a series of articles.
Degeneration of algebraic manifolds and the spectrum of Laplacian
Authors: Yoshikawa Ken-Ichi
Published: July 2016

We shall show that the spectrum of Laplacian depends continuously on the parameter for one parameter degeneration of projective algebraic manifolds.
An explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3
Authors: Katsurada Hidenori
Published: July 2016

Using an induction formula of local densities by Kitaoka, we give an explicit formula for the Fourier coefficients of Siegel Eisenstein series of degree
Transforms on white noise functionals with their applications to Cauchy problems
Authors: Chung Dong Myung , Ji Un Cig
Published: July 2016

A generalized Laplacian ΔG(K) is defined as a continuous linear operator acting on the space of test white noise functionals. Operator-parameter - and -transforms on white noise functionals are introduced and then prove a characterization theorem for and -transforms in terms of the coordinate differential operator and the coordinate multiplication. As an application, we investigate the existence and uniqueness of solution of the Cauchy problem for the heat equation associated with ΔG(K)
Semi-classical bounds on scattering cross sections in two dimensional magnetic fields
Authors: Tamura Hideo
Published: July 2016

We prove the uniform boundedness of averaged total cross sections or of quantities related to scattering into cones in the semi-classical limit for scattering by two dimensional magnetic fields. We do not necessarily assume that the energy under consideration is in a non-trapping energy range in the sense of classical dynamics.
Siegel modular forms and theta series attached to quaternion algebras II
Authors: Böcherer S. , Schulze-Pillot R.
Published: July 2016

We continue our study of Yoshida’s lifting, which associates to a pair of automorphic forms on the adelic multiplicative group of a quaternion algebra a Siegel modular form of degree 2. We consider here the case that the automorphic forms on the quaternion algebra correspond to modular forms of arbitrary even weights and square free levels; in particular we obtain a construction of Siegel modular forms of weight 3 attached to a pair of elliptic modular forms of weights 2 and 4.
Fourier coefficients and Hecke eigenvalues
Authors: Kohnen Winfried
Published: July 2016

We will give certain asymptotic relations between p-eigenvalues and certain Fourier coefficients of Siegel cusp forms of genus g. In particular, it will turn out that potential strong bounds for the Fourier coefficients will imply potential strong bounds for the eigenvalues.
On twisting operators and newforms of half-integral weight II – Complete theory of newforms for Kohnen space
Authors: Ueda Masaru
Published: July 2016

The author continues his previous work with the purpose of establishing a theory of newforms in the case of half-integral weight. In this paper, the author formulates and proves a complete theory of newforms for Kohnen space. Kohnen space is an important canonical subspace in the space of cusp forms of half-integral weight k + 1/2 (k > 0). Every Hecke common eigenform in Kohnen space corresponds to a primitive form of integral weight 2k and of odd level via Shimura Correspondence.

These newforms for Kohnen space satisfy the Strong multiplicity One theorem. Moreover, we explicitly determine the corresponding primitive form (of weight 2k) to each newform for Kohnen space. The space of oldforms is also explicitly described.

In order to find all newforms for Kohnen space, the author needs a certain non-vanishing property of Fourier coefficients of cusp forms. Such property proves by using representation theory of finite linear groups. The method of proof of newform theory is mainly based on trace formulae and trace relations.
Transformations on white noise functions associated with second order differential operators of diagonal type
Authors: Chung Dong Myung , Ji Un Cig , Obata Nobuaki
Published: July 2016

A generalized number operator and a generalized Gross Laplacian are introduced on the basis of white noise distribution theory. The equicontinuity is examined and associated one-parameter transformation groups are constructed. An infinite dimensional analogue of ax + b group and Cauchy problems on white noise space are discussed.
A Remark on Frobenius Extensions and Endomorphism Rings
Authors: Nakayama Tadasi , Tsuzuku Tosiro
Published: July 2016

In his paper [1] F. Kasch developed a theory of Frobenius extensions as a generalization of the theory of Frobenius algebras. In it he established a very interesting relationship between the Frobenius property of an extension and that of its endomorphism ring [1, Satz 5], from which he further derived the Frobenius extension property of Galois extensions of simple rings [1, Satz 6]; with these results he kindly responded to what had been vaguely “conjectured” (as he wrote) by one of the writers on the connection between Galois theory and the theory of Frobenius algebras [2].
Sur La Classification Des Espaces Fibrés Vectoriels Holomorphes Sur Un Tore Complexe Admettant Des Connexions Holomorphes
Authors: Morimoto Akihiko
Published: July 2016

Dans ce travail nous étudierons le problème de classifier les espaces fibres principaux holomorphes de groupe GL(m, C) sur un tore complexe admettant des connexions holomorphes i.e. la classification des espaces fibres vectoriels holomorphes sur un tore complexe admettant des connexions holomorphes. Récemment M. Matsushima [6] a démontré qu’un espace fibré vectoriel holomorphe sur un tore complexe admettant une connexion holomorphe de fibre de dimension 2 possède nécessairement une connexion holomorphe intégrable c.à.d. une connexion holomorphe dont la forme de courbure est nulle. D’autre part d’après Atiyah [1] on sait qu’un espace fibré holomorphe de base M et de groupe structural G admettant une connexion holomorphe intégrable est uu espace fibré principal associé au revêtement universel de la base M par une représentation du groupe fondamental de M dans G et vice versa.
On the Volume in Homogeneous Spaces
Authors: Kurita Minoru
Published: July 2016

Guldin-Pappus’s theorem about the volume of a solid of rotation in the euclidean space has been generalized in two ways. G. Koenigs [1] and J. Hadamard [2] proved that the volume generated by a 1-parametric motion of a surface D bounded by a closed curve c is equal to where are quantities attached to D with respect to a rectangular coordinate system, while are quantities determined by our motion.
On Subsurfaces of Some Riemann Surfaces
Authors: Matsumoto Kikuji
Published: July 2016

In the theory of meromorphic functions, it is important to investigate the properties of covering surfaces generated by their inverse functions. For this purpose, the study of properties of a non-compact region of a Riemann surface is useful.
Tensor products of matrix factorizations
Authors: Yoshino Yuji
Published: July 2016

Let K be a field and let f ∈ K[[x1, x2,…,xr]] and g ∈ K[[y1, y2,…,ys]] be non-zero and non-invertible elements. If X (resp. Y) is a matrix factorization of f (resp. g), then we can construct the matrix factorization X ⊗̂ Y of f + g over K[[x1, x2,…,xr, y1, y2,…,ys]], which we call the tensor product of X and Y.

After showing several general properties of tensor products, we will prove theorems which give bounds for the number of indecomposable components in the direct decomposition of X ⊗̂ Y.
Extension of CR structures on three dimensional pseudoconvex CR manifolds
Authors: Cho Sanghyun
Published: July 2016

Letbe a smoothly bounded orientable pseudoconvexCRmanifold of finite type anddimℝM= 3. Then we extend the givenCRstructure onMto an integrable almost complex structure onwhich is the concave side ofMandM⊂
Very ampleness of adjoint linear systems on smooth surfaces with boundary
Authors: Maşek Vladimir
Published: July 2016

Let M be a ℚ-divisor on a smooth surface over ℂ. In this paper we give criteria for very ampleness of the adjoint of [M], the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of Fujita’s Conjecture in dimension 3.) In §4 we discuss an example which suggests that this kind of criteria might also be useful in the study of linear systems on surfaces.
Z-graduations de type parabolique et polynomes harmoniques
Authors: Mortajine Abdel Latif
Published: July 2016

We give pluriharmonic and harmonic representations of prehomogeneous vector spaces of regular classical parabolic type (L = Γ×M, V) througt the commutative quotients V ‖ M = spec(C[V]M) of them.
Hilbert-Asai Eisenstein series, regularized products, and heat kernels
Authors: Jorgenson Jay , Lang Serge
Published: July 2016

In a famous paper, Asai indicated how to develop a theory of Eisenstein series for arbitrary number fields, using hyperbolic 3-space to take care of the complex places. Unfortunately he limited himself to class number 1. The present paper gives a detailed exposition of the general case, to be used for many applications. First, it is shown that the Eisenstein series satisfy the authors’ definition of regularized products satisfying the generalized Lerch formula, and the basic axioms which allow the systematic development of the authors’ theory, including the Cramér theorem. It is indicated how previous results of Efrat and Zograf for the strict Hilbert modular case extend to arbitrary number fields, for instance a spectral decomposition of the heat kernel periodized with respect to SL2 of the integers of the number field. This gives rise to a theta inversion formula, to which the authors’ Gauss transform can be applied. In addition, the Eisenstein series can be twisted with the heat kernel, thus encoding an infinite amount of spectral information in one item coming from heat Eisenstein series. The main expected spectral formula is stated, but a complete exposition would require a substantial amount of space, and is currently under consideration.
Uniqueness problem with truncated multiplicities in value distribution theory, II
Authors: Fujimoto Hirotaka
Published: July 2016

Let H1, H2,…,Hq be hyperplanes in PN (ℂ) in general position. Previously, the author proved that, in the case where q ≥ 2N + 3, the condition ν(f,Hj) = ν(g, Hj) imply f = g for algebraically nondegenerate meromorphic maps f, g: ℂn → PN(ℂ), where ν(f, Hj) denote the pull-backs of Hj through f considered as divisors. In this connection, it is shown that, for q ≥ 2N + 2, there is some integer ℓ0 such that, for any two nondegenerate meromorphic maps f, g: ℂn → PN(ℂ) with min(ν(f, Hj),ℓ0) = min(ν(g, Hj), ℓ0) the map f × g into PN(ℂ) × PN(ℂ) is algebraically degenerate. He also shows that, for N = 2 and q = 7, there is some ℓ0 such that the conditions min(ν(f, Hj), ℓ0) = min(ν(g, Hj), ℓ0) imply f = g for any two nondegenerate meromorphic maps f, g into P2(ℂ) and seven generic hyperplanes Hj’s.
On the transformation group of the second Painlevé equation
Authors: Umemura Hiroshi
Published: July 2016

We show that for the second Painlevé equation y″ = 2y3 + ty + α, the Bäcklund transformation group G, which is isomorphic to the extended affine Weyl group of type Â1, operates regularly on the natural projectification χ(c)/ℂ(c, t) of the space of initial conditions, where c = α - 1/2. χ(c)/ℂ(c, t) has a natural model χ[c]/ℂ(t)[c]. The group G does not operate, however, regularly on χ[c]/ℂ(t)[c]. To have a family of projective surfaces over ℂ(t)[c] on which G operates regularly, we have to blow up the model χ[c] along the projective lines corresponding to the Riccati type solutions.
A recurrence formula for q-Bernoulli numbers attached to formal group
Authors: Satoh Junya
Published: July 2016

Kaneko [2] proved a new recurrence formula for the Bernoulli numbers and gave two proofs. One of them was due to Don Zagier. We shall apply Zagier’s idea to the g-Bernoulli numbers attached to formal group.
On the classification of 3-dimensionalSL2(ℂ)-varieties
Authors: Kebekus Stefan
Published: July 2016

In the present work we describe 3-dimensional complexSL2-varieties where the genericSL2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group acts such that the generic orbits are 2-dimensional.

This is an ingredient of the classification [Keb99] of the 3-dimensional relatively minimal quasihomogeneous varieties where the automorphism group is not solvable.
A remark on the theorem of Ohsawa-Takegoshi
Authors: Diederich Klas , Mazzilli Emmanuel
Published: July 2016

If D ⊂ ℂn is a pseudoconvex domain and X ⊂ D a closed analytic subset, the famous theorem B of Cartan-Serre asserts, that the restriction operator r : (D) → (X) mapping each function F to its restriction F|X is surjective. A very important question of modern complex analysis is to ask what happens to this result if certain growth conditions for the holomorphic functions on D and on X are added.
Multipliers on vector spaces of holomorphic functions
Authors: Render Hermann , Sauer Andreas
Published: July 2016

LetGbe a domain in the complex plane containing zero andH(G) be the set of all holomorphic functions onG. In this paper the algebraM(H(G)) of all coefficient multipliers with respect to the Hadamard product is studied. Central for the investigation is the domainintroduced by Arakelyan which is by definition the union of all setswithw∈ Gc. The main result is the description of all isomorphisms between these multipliers algebras. As a consequence one obtains: If two multiplier algebras M(H(G1)) andM(H(G2)) are isomorphic thenis equal toTwo algebrasH(G1) andH(G2) are isomorphic with respect to the Hadamard product if and only ifG1is equal toG2. Further the following uniqueness theorem is proved: IfG1is a domain containing 0 and ifM(H(G)) is isomorphic toH(G1) thenG1is equal to.
Some Remarks on Symmetric and Frobenius Algebras
Authors: Jans J. P.
Published: July 2016

In [5] we defined the concepts of Frobenius and symmetric algebra for algebras of infinite vector space dimension over a field. It was shown there that with the introduction of a topology and the judicious use of the terms continuous and closed, many of the classical theorems of Nakayama [7, 8] on Frobenius and symmetric algebras could be generalized to the infinite dimensional case. In this paper we shall be concerned with showing certain algebras are (or are not) Frobenius or symmetric. In Section 3, we shall see that an algebra can be symmetric or Frobenius in “many ways”. This is a problem which did not arise in the finite dimensional case.
On the Ring of Integers in an Algebraic Number Field as a representation Module of Galois Group
Authors: Yokoi Hideo
Published: July 2016

1. Introduction. It is known that there are only three rationally inequivalent classes of indecomposable integral representations of a cyclic group of prime order l. The representations of these classes are:

(I) identical representation,

(II) rationally irreducible representation of degree l – 1,

(III) indecomposable representation consisting of one identical representation and one rationally irreducible representation of degree l-1 (F. E. Diederichsen [1], I. Reiner [2]).
Capacitability of Analytic Sets
Authors: Kishi Masanori
Published: July 2016

Let Ω be a locally compact separable metric space and let Ф be a positive symmetric kernel. Then the inner and outer capacities of subsets of Ω are defined by means of Ф-potentials of positive measures in the following manner. We define the capacity c(K) of a compact set K in a certain manner by means of Ф-potentials.
Espaces Homogènes De Stein Des Groupes De Lie Complexes
Authors: Matsushima Yozô
Published: July 2016

A. Soit G un groupe de Lie complexe et connexe et soit K un sous-groupe compact maximal de G. Soient g et les algèbres de Lie de G et K respectivement. est une sous-algèbre réelle de l’algèbre complexe g. Soit (i2 = –1). Alors est une sous-algèbre complexe de g.