bluuebunny/crossref_metadata_2025_split huggingface dataset:
Non ‐ Classical Mixed Interface Problems for Anisotropic Bodies
Authors: Jentsch Lothar , Natroshvili David 
Published: May 2007

AbstractThe paper deals with the three‐dimensional mathematical problems of the elasticity theory of anisotropic piece‐wise homogeneous bodies. Non ‐ classical mixed type boundary value problems are studied when on one part (S1) of the interface the rigid contact conditions (jumps of displacement and stress vectors) are given, while conditions of the non ‐ classical interface Problem H or Problem G are imposed on the remaining part (S2) of the interface, i. e., in both cases jumps of the normal components of displacement and stress vectors are known on S2 and, in addition, in the first one (Problem H) the tangent components of the displacement vector and in the second one (Problem G) the tangent components of the stress vector are given from the both sides on S2.The investigation is carried out by the potential method and the theory of pseudodifferential equations on manifolds with boundary.
Algebras of Singular Integral Operators with Piecewise Continuous Coefficients on Reflexive Orlicz Spaces
Authors: Karlovich Aleksey Yu. 
Published: May 2007

AbstractWe consider singular integral operators with piecewise continuous coefficients on reflexive Orlicz spacesLm(σ) which are generalizations of the Lebesgue spacesLP(σ), 1 < p < ∞. We suppose that σ belongs to a large class of Carleson curves, including curves with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. For the singular integral operator associated with the Riemann boundary value problem with a piecewise continuous coefficientG, we establish a Fredholm criterion and an index formula in terms of the essential range ofGcomplemented by spiralic horns depending on the Boyd indices ofLM(σ) and contour properties. Our main result is a symbol calculus for the closed algebra of singular integral operators with piecewise continuous matrix ‐ valued coefficients onLMn(σ).
On the Size of the Exceptional Set in Nevanlinna's Second Fundamental Theorem for Certain Classes of Meromorphic Functions
Authors: Rodríguez Francisco 
Published: May 2007

AbstractSome conditions on the size of the exceptional set that arise in Nevanlinna's Second Fundamental Theorem are established, showing that previous sharp results can be improved by restricting the class of functions considered and suggesting a close relationship between the size of the exceptional set and the lower growth of the characteristic function. Examples of functions of rapid growth possessing exceptional sets are built, showing that these conditions are sharp for the class of functions considered.
Spectral Decomposition of Symmetric Operator Matrices
Authors: Mennicken Reinhard , Shkalikov Andrey A. 
Published: May 2007

AbstractThe authors study symmetric operator matricesmagnified imagein the product of Hilbert spaces H = H1×H2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure Lo exists and is a selfadjoint operator in H. With Lo, the closure of the transfer functionmagnified imageis considered. Under the assumption that there exists a real number β < inf p(A) such that M(β)<< 0, it follows that β ε p(Lo). Applying a factorization result of A.I. Virozub and V.I. Matsaev [VM] to the holomorphic operator function M(λ, the_spectral subspaces of Lo corresponding to the intervals ] — ∞, β] and [β, ∞[ and the restrictions of Lo to these subspaces are characterized. Similar results are proved for operator matricesmagnified imagewhich are symmetric in a Krein space.
Spectral Analysis for Linear Pencils N — λP of Ordinary Differential Operators
Authors: Shkalikov Andrey A. , Tretter Christiane 
Published: May 2007

AbstractBoundary eigenvalue problems for linear pencils N — λ of two ordinary differential operators are studied where P is of lower order than N. In a suitable scale of subspaces of Sobolev spaces and spaces of continuously differentiable functions results on minimality and basis properties of the eigenfunctions and associated functions are proved, including explicit formulas for the Fourier coefficients. As an application the Orr ‐ Sommerfeld equation is considered.
Instability Phenomena for the Fourier Coefficients
Authors: Aizenberg Lev , Tarkhanov Nikolai 
Published: May 2007

AbstractLet P be an elliptic differential operator on a non‐compact connected manifold X; suppose that both X and the coefficients of P are real analytic. Given a pair of open sets D and σ in X with σ⊂⊂ D ⊂⊂ X, we fix a sequence {ev} of solutions of Pu = 0 in D which are pairwise orthogonal under integration over both D and σ. By orthogonality is meant the orthogonality in the corresponding Sobolev spaces; we also assume a completeness of the system on σ. For a fixed y ε X/⊂, denote by kv(y) the Fourier coefficients of a fundamental solution ϕ(·, y) of P with respect to the restriction of {ev} to σ. Suppose K is a compact set in D/σ, and let f be a distribution with support on K. In this paper we show, under appropriate conditions on K, that if the moments (f, kv) decrease sufficiently rapidly in a certain precise sense, then these moments vanish identically. In the most favorable cases, it is then possible to conclude that f = 0. This phenomenon was previously noticed by the first author and L. Zalcman for analytic and harmonic moments of f.
The Trace Formula for Schrödinger Operators from Infinite Dimensional Oscillatory Integrals
Authors: Albeverio Sergio , De Monvel‐Berthier Anne Boutet , Brzeźniak Zdzislaw 
Published: May 2007

AbstractThe theory of infinite dimensional oscillatory integrals by finite dimensional approximations is shown to provide new information on the trace formula for Schrödinger operators. In particular, the explicit computation of contributions given by constant and non constant periodic orbits, for potentials which are quadratic plus a bounded nonlinear part, is provided. The heat semigroup as well as the Schrödinger group are discussed and it is shown in particular that their singular supports are contained in an explicit countable set independent of the bounded part of the potential.
Regular Sturm ‐ Liouville Problems Whose Coefficients Depend Rationally on the Eigenvalue Parameter
Authors: De Snoo Henk 
Published: May 2007

AbstractIn this note we consider regular Sturm‐Liouville equations with a floating singularity of a special type: the coefficient of the second order derivative contains the eigenvalue parameter. We determine the form of the boundary conditions which make the problem selfadjoint after linearizing. In general the boundary conditions for the linearized system give rise to boundary conditions which involve the eigenvalue parameter in the original, non‐linearized, problem. The boundary conditions give rise to a 2 × 2 matrix function, the so‐called Titchmarsh‐Weyl coefficient. The characteristic properties of this function are studied. The formal aspects of the theory of this class of equations turn out to be quite parallel to those for the usual situation when there is no floating singularity.
On Some Properties of the Solutions of Quasilinear Degenerate Elliptic Equations
Authors: Kondratiev Wladimir , Nicolosi Francesco 
Published: May 2007

AbstractWe prove the existence of bounded solutions of some boundary value problems for degenerate elliptic equations of second order in divergence form. Our results cover also the unbounded domain case. We discuss also the uniqueness problem and asymptotic behaviour of the solutions of our equation.
Asymptotics of the Spectrum of Douglis ‐ Nirenberg Elliptic Operators on a Compact Manifold
Authors: Kozhevnikov Alexander 
Published: May 2007

AbstractPseudo‐ differential systems on closed manifolds, elliptic in the sense of DOUGLIS and Nirenberg. are considered. It is proved that the system is similar to an diagonal operator up to an operator of order ‐ ∞, and the similarity transformation preserves ellipticity and parameter ‐ellipticity. The similarity transformation may be chosen so that it preserves even self adjointness up to an operator of order less than the lowest order of the diagonal entry. These results are applied to prove the eigenvalue asymptotics with the sharp estimate of the remainder in the self adjoint case as well as a rough asymptotics in the non‐self‐adjoint case. Another application is the eigenvalue asymptotics with the sharp estimate of the remainder for general self‐ adjoint elliptic boundary value problems with the spectral parameter appearing linearly in boundary conditions.
On the Nonoscillatory Behavior of Solutions of a Second Order Linear Differential Equation
Authors: Li Horng‐Jaan , Yeh Cheh‐Chih 
Published: May 2007

AbstractIn this paper, wo improve the Sturm comparison theorem and two nonoscillation criteria of Leighton and Wintner, and establish two variants of a Wintner' s nonoscillatory criterion of the second order linear differential equation magnified image where r, c : t0,∞) →, R > 0 a. e. on t0,∞) and 1/r, c ε Ll(t0,b) for each b ∞ (t0,>) for some t0 > 0. Using these two criteria, we improve some nonoscillation criteria of Hartman. Hille. Moore. Potter. WintnEr, and Willett. These proofs are more elegant and concise than those of theirs.
A Generalization of the Theorem of Hardy: A Most General Version of the Uncertainty Principle for Fourier Integrals
Authors: Pfannschmidt Christian 
Published: May 2007

AbstractN. Wiener remarked that a non ‐ identically vanishing real function and its Fourier transform cannot both decay “very fast”. It was Hardy who specified and proved this assertion in 1933. In the present paper Hardy's theorem will be generalized. Moreover, it will be shown that further weakening of these assumptions does not make sense.
On Cauchy Homomorphisms of Nearness Frames
Authors: Banaschewski B. , Pultr A. 
Published: May 2007

AbstractTo include the pointfree case, the notion of a Cauchy map easily extends as the condition that the preimage of any regular Cauchy filter contains a regular Cauchy filter. This extension, however, can be unsatisfactory if the regular Cauchy filters are scarce or non‐existent, making the condition too weak, indeed sometimes even void. In this paper a variant of the notion, independent on the existence of any kind of filters, is studied: a homomorphism is called fully Cauchy if it lifts to the completions. This is generally stronger than, and in the spatial and metric cases it coincides with the previously mentioned property. Moreover, it is stable under localization.
Subelliptic Estimates for a Class of Degenerate Elliptic Integro‐Differential Operators
Authors: Cancelier Claudy , Franchi Bruno 
Published: May 2007

AbstractIn this paper we prove subelliptic estimates for operators of the form Δx + λ2 (x)S in ℝN = ℝ × ℝ, where the operator S is an elliptic integro ‐ differential operator in ℝN and λ is a nonnegative Lipschitz continuous function.
On the Boundedness of Pseudo ‐ Differential Operators on Weighted Besov ‐ Triebel Spaces
Authors: Dintelmann Peter 
Published: May 2007

AbstractAn elementary straightforward proof for the boundedness of pseudo ‐ differential operators of the Hörmander class ΨμI,δ on weighted Besov ‐ Triebel spaces is given using a discrete characterization of function spaces.
Half‐Linear Eigenvalue Problems
Authors: Eberhard Walter , Elbert Árpad 
Published: May 2007

AbstractWe consider the eigenvalue problem
magnified image
for t ϵ [0, b], where an = |a|n sgna, a ϵ ℝ, λ ϵ ℝ, the constants μ, v are real such that 0 ≤ μ < n and derive asymptotic estimates for solutions of the differential equation in the definite case q(t)> 0 which corresponds to the well‐known WKB‐approximation in the linear case n = 1, μ = 0. In the second part we investigate the asymptotic distribution of the eigenvalues in the general case of two ‐point boundary conditions and refine these results for the so called separated boundary conditions.
Nonlinear Riemann ‐ Hilbert Problems without Transversality
Authors: Efendiev M. A. , Wendland W. L. 
Published: May 2007

AbstractNonlinear Riemann ‐ Hilbert problems (RHP) generalize two fundamental classical problems for complex analytic functions, namely: 1. the conformal mapping problem, and 2. the linear Riemann ‐ Hilbert problem. This paper presents new results on global existence for the nonlinear (RHP) in doubly connected domains with nonclosed restriction curves for the boundary data. More precisely, our nonlinear (RHP) is required to become „at infinity”︁, i.e., for solutions having large moduli, a linear (RHP) with variable coefficients. Global existence for q‐connected domains was already obtained in [9] for the special case that the restriction curves for the boundary data „at infinity”︁ coincide with straight lines corresponding to linear (RHP)‐s with special so‐called constant ‐ coefficient transversality boundary conditions. In this paper, the boundary conditions are much more general including highly nonlinear conditions for bounded solutions in the context of nontransversality. In order to prove global existence, we reduce the problem to nonlinear singular integral equations which can be treated by a degree theory of Fredholm ‐ quasiruled mappings specifically constructed for mappings defined by nonlinar pseudodifferential operators.
Cusp Forms on GL(2n) with GL(n) × GL (n) Periods, and Simple Algebras
Authors: Flicker Yuval Z. 
Published: May 2007

AbstractThe notion of a period of a cusp form on GL(2,D(𝔸)), with respect to the diagonal subgroup D(𝔸)X × D(𝔸)X, is defined. Here D is a simple algebra over a global field F with a ring 𝔸 of adeles. For Dx = GL(1), the period is the value at 1/2 of the L‐function of the cusp form on GL(2, 𝔸). A cuspidal representation is called cyclic if it contains a cusp form with a non zero period. It is investigated whether the notion of cyclicity is preserved under the Deligne ‐ Kazhdan correspondence, relating cuspidal representations on the group and its split form, where D is a matrix algebra. A local analogue is studied too, using the global technique. The method is based on a new bi‐period summation formula. Local multiplicity one statements for spherical distributions, and non ‐ vanishing properties of bi ‐ characters, known only in a few cases, play a key role.
The Quantization of the Cantor Distribution
Authors: Graf S. , Luschgy H. 
Published: May 2007

AbstractFor a real‐valued random variable whose distribution is the classical Cantor probability, the n ‐ quantization error and the n ‐ optimal quantization rules are calculated for every natural number n. Moreover, the connection between the rate of convergence of the logarithms of the quantization errors for n going to infinity and the Hausdorff dimension of the Cantor set is indicated.
On Hardy ‐ Littlewood Maximal Functions in Orlicz Spaces
Authors: Kita H. 
Published: May 2007

AbstractLet Φ(t) and Ψ(t) be the functions having the following representations Φ(t) = ∫a(s)ds and Ψ(t) = ∫b(s) ds, where a(s) is a positive continuous function such that ∫a(s)/s ds = + ∞ and b(s) is an increasing function such that lims→ ∞ b(s) = + ∞. Then the following statements for the Hardy ‐ Littlewood maximal function M f (x) are equivalent:
(i) there exist positive constants c1 and s0 such that magnified image
(ii) there exist positive constant c2 and c3 such thatmagnified image
.
Powerful Necessary Conditions for Class Number Problems
Authors: Louboutin Stéphane 
Published: May 2007

AbstractWe give a necessary condition for the ideal class group of a CM‐field to be of exponent at most two. This condition enables us to drastically reduce the amount of relative class number computation for determination of the CM ‐ fields of some types (e. g. the imaginary cyclic non ‐quadratic number fields of 2 ‐ power degrees) whose ideal class groups are of exponents at most two. We also give a necessary condition for some quartic non ‐ CM ‐ fields to have class number one.
On the Embedded Eigenvalues and Dense Point Spectrum of the Stark‐Like Hamiltonians
Authors: Naboko Sergei N. , Pushnitski Alexander B. 
Published: May 2007

AbstractThe point spectrum lying on the essential spectrum is investigated for the one‐dimensional Schrödinger operator \documentclass{article}\pagestyle{empty}\begin{document}$ \- \frac{{d^2 }}{{dx^2 }} + q(x) $\end{document} with decaying potential q, and weakly perturbed Stark‐like operator \documentclass{article}\pagestyle{empty}\begin{document}$ - \frac{{d^2 }}{{dx^2 }} - \left| x \right|^\alpha {\rm sign }x + q(x). $\end{document} An elementary constructive technique is developed to obtain various results concerning embedded eigenvalues of Schrödinger operators. In Section 3 a constructive example of the Stark ‐ like operator with the potential q decaying slightly slowlier than o(1/|x|1‐α/2)and dense point spectrum on the whole real axis is presented.
Some Remarks on the Boundedness of Pseudodifferential Operators
Authors: Shargorodsky Eugene 
Published: May 2007

AbstractSome methods are described for reducing the problem of the boundedness of pseudodifferential operators (ΨDOs) to the theory of Fourier multipliers. Special attention is given to the boundedness of ΨDOs in Besov ‐ Triebel ‐ Lizorkin spaces.
Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators
Authors: Stolz G. 
Published: May 2007

AbstractThe absolutely continuous and singular spectrum of one‐dimensional Schrödinger operators with slowly oscillating potentials and perturbed periodic potentials is studied, continuing similar investigations for Jacobi matrices from [14]. Trace class methods are used to locate the singular spectrum. The absolutely continuous spectrum is determined by iterated diagonalization of transfer matrices to prove boundedness of eigensolutions.
Gevrey Asymptotic Representation of the Solutions of Equations with One Turning Point
Authors: Yagdjian Karen 
Published: May 2007

AbstractAn ordinary differential equation of the type
magnified image
with parameterξ ϵ IRn and smooth coefficients aj,a ϵ C∞([‐T,T]) is studied. It is assumed that all the characteristic roots of the equation vanish at t = 0 while for t ≠ 0 they are real and distinct. The constructions of real‐valued phase functions ϕpHkl (k,l = 1., m) and of amplitude functions Ajkl such that for a given s ϵ [‐T, T] every solution u(t, ξ) of the equation can be represented as magnified image
where Ψj(s, ξ)= Djtu(s,ξ), j = 0,m‐1 are given.
ℋ︁ — Cohomologies Versus Algebraic Cycles
Authors: Viale Luca Barbieri 
Published: May 2007

AbstractGlobal intersection theories for smooth algebraic varieties via products in appropriate Poincaré duality theories are obtained. We assume given a (twisted) cohomology theory H* having a cup product structure and we consider the ℋ︁‐ cohomology functor X ↝ H#Zar(X, ℋ︁*) whereℋ︁* is the Zariski sheaf associated to H*. We show that the ℋ︁‐ cohomology rings generalize the classical “intersection rings” obtained via rational or algebraic equivalences. Several basic properties e. g. Gysin maps, projection formula and projective bundle decomposition, of ℋ︁‐ cohomology are obtained. We therefore obtain, for X smooth, Chern classes cP, i :Ki(X)→ Hp‐i(X,ℋ︁ p) from the Quillen K‐theory to ℋ︁‐ cohomologies according to Gillet and Grothendieck. We finally obtain the “blow‐up formula” magnified image where X′ is the blow–up of X smooth, along a closed smooth subset Z of pure codimension c. Singular cohomology of associated analityc space, étale cohomology, de Rham and Deligne–Beilinson cohomologies are examples for this setting.
Bounds for the Genus of Space Curves
Authors: Beorchia Valentina 
Published: May 2007

AbstractWe compute the following upper bounds for the maximal arithmetic genus Pa(d,t) over all locally Cohen ‐ Macaulay space curves of degree d, which are not contained in a surface of degree magnified image These bounds are sharp for t ≤ 4 abd any d ≥ t.
Anisotropic Edge Pseudo — Differential Operators with Discrete Asymptotics
Authors: Buchholz Thilo 
Published: May 2007

AbstractAn anisotropic pseudo — differential calculus aimed at solving parabolic differential and pseudo — differential equations in terms of Volterra pseudo–differential operators was studied by Piriou for spatial variables on a closedC∞– manifold. Such a program also makes sense when the spatial variables run over a manifold with edges. Our approach deals with this case. It covers, in particular, manifolds with conical singularities. The main point of the present paper is the anisotropic edge pseudo — differential calculus, obtained as a substructure of our corresponding abstract anisotropic edge calculus with operator — valued symbols.
Zur Zerlegung von Primelementen quadratischer Zahlkörper in relativ–quadratischen Oberkörpern
Authors: Burde Klaus 
Published: May 2007

AbstractFür gewisse quadratische Erweiterungen wird ein geometrisch interpretierbares Kriterium dafür angegeben, ob ein ungerades Primelement von verzweigt, zerfällt oder träge ist.
On Indefinite Moment Problems and Resolvent Matrices of Hermitian Operators in Kreîn Spaces
Authors: Derkach Vladimir 
Published: May 2007

AbstractLet (sj)∞j=0 be a sequence of real numbers such that the Hankel matrices (si+j)∞0, (Si+j+i)∞0 have finite numbers of negative eigenvalues. The indefinite moment problem with the moments Sj (j = 0,1,2, …) and the corresponding Stieltjes string are investigated. We use the approach via the Kreîn — Langer extension theory of symmetric operators in spaces with indefinite metric. In the framework of this approach a description of L– resolvents of a class of symmetric operators in Kreîn space and a simple formula for the calculation of the L– resolvent matrix in terms of boundary operators are given.
The Distribution of Reciprocal Pairs Modulo Polynomials over a Finite Field
Authors: Hensley Doug 
Published: May 2007

AbstractGiven a finite field Fq of order q, a fixed polynomial g in –Fq[X] of positive degree, and two elements u and v in the ring of polynomials in R = Fq [X]/gFq[X], the question arises: How many pairs (a, 6) are there in R × R so that ab  1 mod g and so that a is close to u while b is close to v ? The answer is, about as many as one would expect. That is, there are no favored regions in R × R where inverse pairs cluster. The error term is quite sharp in most cases, being comparable to what would happen with random distribution of pairs. The proof uses Kloosterman sums and counting arguments. The exceptional cases involve fields of characteristic 2 and composite values of g. Even then the error term obtained is nontrivial. There is no computational evidence that inverses are in fact less evenly distributed in this case, however.
Resolvent Estimates for Singularly Perturbed Elliptic Operators in Hölder Spaces
Authors: Najman Branko 
Published: May 2007

AbstractThe norm of the inverse operator of ϵA + B ‐ λI between the Besov spaces B, ∞ (Ω) and Bt∞,∞(Ω) is estimated, where A and B are uniformly elliptic operators with smooth coefficients and Dirichlet boundary conditions, A is of order 2m, B of order 2m, m > m'. The estimate holds for negative t. The Besov space B, ∞ (Ω) reduces to the space of Hölder continuous functions Cs (Ω) if s < 0 is non – integer.In particular, it is shown that Aϵ generates an analytic semigroup in B, ∞ (Ω), s ϵ (‐1,0), if Ω = ℝn or ℝ and A, B are constant coefficient operators without lower order terms.
Singularities in Quasi–Banach Spaces with Applications to Semilinear Elliptic Equations II
Authors: Runst Thomas 
Published: May 2007

AbstractThis paper continues the investigation about the singularity theory in dual rich quasi–Banach spaces given in T. Runst [Ru 2]. The abstract results are applied to the study of the solution structure of semilinear elliptic boundary value problems in spaces of Besov – Triebel – Lizorkin type.