bluuebunny/crossref_metadata_2025_split huggingface dataset:
Integral operators involving Whittaker functions
Authors: Nasim C. 
Published: May 2009

We define the integral operators and asandwhereand Wk, u and Mk, u are the Whittaker's confluent hyper-geometric functions. These operators, in their slightly less general form, have been dealt with in [2] and [4]. There the authors have used the fact that these integral operators can be expressed as compositions of the Kober's fractional integral operators and the modified Laplace operator. Then these operators are inverted accordingly. Generally, this type of technique has been very useful for inverting many kinds of integral equations; and a good account of the procedures involved is given [5].
On an inversion formula
Authors: Naylor D. 
Published: May 2009

In this paper the author considers the problem of finding a formula of inversion for the integral transform defined by the equationwhere a >0, k > 0 and r-1f(r) εL (a, ∞). This transform appeared in connection with an earlier investigation [4] in which an attempt was made to devise an integral transform that could be adapted to the solution of certain boundary value problems involving the space form of the wave equation and the condition of radiation:
Convexity conditions for non-locally convex lattices
Authors: Kalton N. J. 
Published: May 2009

First we recall that a (real) quasi-Banach space X is a complete metrizable real vector space whose topology is given by a quasi-norm satisfyingwhere C is some constant independent of x1 and x2. X is said to be p-normable (or topologically p-convex), where 0 < p ≤ l, if for some constant B we havefor any x1, …, xn, є X. A theorem of Aolci and Rolewicz (see [18]) asserts that if in C = 21/p-1, then X is p-normable. We can then equivalently re-norm X so that in (1.4) B = 1.
Cousin complexes and generalized fractions
Authors: Riley Adrian M. , Sharp Rodney Y. , Zakeri Hossein 
Published: May 2009

Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [6, §2]: it is a complex of A-modules and A-homomorphismswith the property that, for each n≥0,Cohen-Macaulay rings may be characterized in terms of the Cousin complex: A is a Cohen-Macaulay ring if and only if C(A) is exact [6, (4.7)]. Also the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring: see [6, (5.4)].
On the order of automorphism groups of Klein surfaces
Authors: Gordejuela J. J. Etayo 
Published: May 2009

A problem of special interest in the study of automorphism groups of surfaces are the bounds of the orders of the groups as a function of the genus of the surface.May has proved that a Klein surface with boundary of algebraic genus p has at most 12(p–1) automorphisms [9].In this paper we study the highest possible prime order for a group of automorphisms of a Klein surface. This problem was solved for Riemann surfaces by Moore in [10]. We shall use his results for studying the Klein surfaces that are not Riemann surfaces. The more general result that we obtain is the following: if X is a Klein surface of algebraic genus p, and G is a group of automorphisms of X, of prime order n, then n ≤ p + 1.
On groups which are the product of abelian subgroups
Authors: Amberg Bernhard 
Published: May 2009

If the group G=AB is the product of two abelian subgroups A and B, then G is metabelian by a well-known result of Itô [8], so that the commutator subgroup G' of G is abelian. In the following we are concerned with the following condition:There exists a normal subgroupwhich is contained in A or B.Recently, Holt and Howlett in [7] have given an example of a countably infinite p-group G = AB, which is the product of two elementary abelian subgroups A and B with Core(A) = Core (B) = 1, so that in this group (*) does not hold. Also, Sysak in [13] gives an example of a product G = AB of two free abelian subgroups A and B with Core(A)=Core(B)=l.
The Fourier transform of vector-valued functions
Authors: Okada Susumu 
Published: May 2009

For each natural numbern, letun(x)=(1—cosnx)/πnx2(xɛℝ). It is well–known that a bounded continuous functionfon the real line ℝ is the Fourier transform of an integrable function on ℝ if and only if the functions Φn(f) (n= 1, 2,…), defined byform a Cauchy sequence in the spaceL1(ℝ) (cf. [2]). Such a characterization, which can be extended to functions defined on a locally compact Abelian group more general than ℝ, is based on the fact that the spaceL1(ℝ) is complete with respect to convergence in mean.
Dirichlet and Poincaré series
Authors: Good A. 
Published: May 2009

The study of modular forms has been deeply influenced by famous conjectures and hypotheses concerningwhere T(n) denotes Ramanujan's function. The fundamental discriminant Δ is a cusp form of weight 12 with respect to the modular group. Its associated Dirichlet seriesdefines an entire function of s and satisfies the functional equationThe most penetrating statements that have been made on T(n) and LΔ(s)are:Of these four problems only A1 has been established so far. This was done by Deligne [1] using methods from algebraic geometry and number theory. While B1 trivially holds with ε > 1/2, it was established in [2] for every ε>1/3. Serre [12] proved A2 for a positive proportion of the integers and Hafner [5] showed that LΔ has a positive proportion of its non-trivial zeros on the line σ=6. The proofs of the last three results are largely analytic in nature.
Trace rings of generic matrices are unique factorization domains
Authors: Bruyn Lieven Le 
Published: May 2009

A. W. Chatters and D. A. Jordan defined in [0] a unique factorization ring to be a prime ring in which every height one prime ideal is principal. In this note we will prove that the trace ring of m generic n × n-matrices satisfies this condition.Throughout this note, k will be a field of characteristic zero. Consider the polynomial ring S = k[;1≤i, j≤n, 1≤l≤m] and the n × n matrices Xl = in Mn(S). The k-subalgebra of Mn(S) generated by {Xl; 1≤l≤m} is called the ring of m generic n × n matrices Gm,n. Adjoining to it the traces of all its elements we obtain the trace ring of m n × n generic matrices, cfr. e.g. [1].
Spectral properties of holomorphic automorphism with fixed point
Authors: Mazur T. , Skwarczyński M. 
Published: May 2009

The Hilbert space methods in the theory of biholomorphic mappings were applied and developed by S. Bergman [1, 2]. In this approach the central role is played by the Hilbert spaceL2H(D)consisting of all functions which are square integrable and holomorphic in a domainD ⊂ ℂN. A biholomorphic mapping φ:D ⃗ Ginduces the unitary mappingUφ:L2H(G)⃗L2H(D)defined by the formulaHere ∂φ/∂z denotes the complex Jacobian of φ. The mappingUϕis useful, since it permits to replace a problem forDby a problem for its biholomorphic imageG(see for example [11], [13]). When ϕ is an automorphism ofDwe obtain a unitary operatorUϕonL2H(D).
Spectral operators and weakly compact homomorphisms in a class of Banach Spaces
Authors: Ricker W. 
Published: May 2009

The purpose of this note is to present certain aspects of the theory of spectral operators in Grothendieck spaces with the Dunford-Pettis property, briefly, GDP-spaces, thereby elaborating on the recent note [10].For example, the sum and product of commuting spectral operators in such spaces are again spectral operators (cf. Proposition 2.1) and a continuous linear operator is spectral if and only if it has finite spectrum (cf. Proposition 2.2). Accordingly, if a spectral operator is of finite type, then its spectrum consists entirely of eigenvalues. Furthermore, it turns out that there are no unbounded spectral operators in such spaces (cf. Proposition 2.4). As a simple application of these results we are able to determine which multiplication operators in certain function spaces are spectral operators.
Clifford division algebras and anisotropic quadratic forms: two counterexamples
Authors: Mammone P. , Tignol J. P. 
Published: May 2009

In a recent paper [3], D. W. Lewis proposed the following conjecture. (The notation is the same as that in [2] and [3].)Conjecture. Let F be a field of characteristic not 2 and let a1, b1…, an, bn ∈ Fx. The tensor product of quaternion algebrasis a division algebra if and only if the quadratic form over Fis anisotropic.This equivalence indeed holds for n = 1 as is well known [2, Theorem 2.7], and Albert [1] (see also [4, §15.7]) has shown that it also holds for n = 2. The aim of this note is to provide counterexamples to both of the implications for n ≥ 3.
Macbeath's Curve and the Modular Group
Authors: Wohlfahrt K. 
Published: May 2009

On p. 244 of Glasgow Math. J.27 (1985) on the right hand side of one of the 6 equations characterizing the 4 fixed points of the involution v a sign error has occurred.The relevant equation should ready0y3y5y6=–1,or the points would not lie on the curve.Correcting the error unfortunately invalidates the model of an elliptic curve given in §6, which therefore has to be re-evaluated. First we find, in the notation of the paper,2 f (x) = ((r + 1)/(R + 2))2.
Coperfect monoids
Authors: Gould Victoria 
Published: May 2009

Throughout this paper S will denote a given monoid, that is, a semigroup with an identity. A set A is a right S-system if there is a map φ: A × S → A satisfyingfor any element a of A and any elements s, t of S. For φ(a, s) we write as and we refer to right S-systems simply as S-systems. One has the obvious definitions of an S-subsystem and an S-homomorphism.
Estimates for a remainder term associated with the sum of digits function
Authors: Foster D. M. E. 
Published: May 2009

If q(≥2) is a fixed integer it is well known that every positive integer k may be expressed uniquely in the formWe introduce the ‘sum of digits’ functionBoth the above sums are of course finite. Although the behaviour of α(q, k) is somewhat erratic, its average behaviour is more regular and has been widely studied.
On the classification of isotropic tensors
Authors: Appleby P. G. , Duffy B. R. , Ogden R. W. 
Published: May 2009

A tensor is said to be isotropic relative to a group of transformations if its components are invariant under the associated group of coordinate transformations. In this paper we review the classification of tensors which are isotropic under the general linear group, the special linear (unimodular) group and the rotational group. These correspond respectively to isotropic absolute tensors [4, 8] isotropic relative tensors [4] and isotropic Cartesian tensors [3]. New proofs are given for the representation of isotropic tensors in terms of Kronecker deltas and alternating tensors. And, for isotropic Cartesian tensors, we provide a complete classification, clarifying results described in [3].In the final section of the paper certain derivatives of isotropic tensor fields are examined.
Some projective representations of finite abelian groups
Authors: Morris A. O. , Saeed-Ul-Islam M. , Thomas E. 
Published: May 2009

In this paper, we continue the work initiated by Morris [5] and Saeed-ul-Islam [6,7] and determine complete sets of inequivalent irreducible projective representations (which we shall write as i.p.r.) of finite Abelian groups with respect to some additional factor sets.We consider an Abelian groupwhich will be referred to as an Abelian group of type (a1, …, am).
Toeplitz operators on abstract Hardy spaces
Authors: Smith R. C. 
Published: May 2009

In [10], C. Sundberg uses a clever argument involving an idea of Davie and Jewell [13] to prove an isomorphism theorem for a very general class of operators. A related spectral inclusion theorem is an immediate consequence of the proof of this result, as Sundberg points out. He goes on to list several well known examples that are applications of his main result and remarks that the proof of the McDonald–Sundberg theorem (c.f. [9]) can now be considerably simplified. The purpose of this note is to give further evidence of the utility of the criterion established in [10]. Here and throughout X denotes a compact Hausdorff space and A is a function algebra on X. The Shilovboundary of A is the minimal closed subset ∂(A) of X with the property that.
Coordinates for analytic operator algebras
Authors: Solel Baruch 
Published: May 2009

Let M be a σ-finite von Neumann algebra and α = {αt}t∈A be a representation of a compact abelian group A as *-automorphisms of M. Let Γ be the dual group of A and suppose that Γ is totally ordered with a positive semigroup Σ⊆Γ. The analytic algebra associated with α and Σ iswhere spα(a) is Arveson's spectrum. These algebras were studied (also for A not necessarily compact) by several authors starting with Loebl and Muhly [10].
A result on hermitian operators
Authors: Jamison J. E. , Lin Pei-Kee 
Published: May 2009

Let X be a complex Banach space. For any bounded linear operator T on X, the (spatial) numerical range of T is denned as the setIf V(T) ⊆ R, then T is called hermitian. Vidav and Palmer (see Theorem 6 of [3, p. 78] proved that if the set {H + iK:H and K are hermitian} contains all operators, then X is a Hilbert space. It is natural to ask the following question.
Small isomorphisms between group algebras
Authors: Wood G. V. 
Published: May 2009

If G1 and G2 are locally compact groups and the algebras Ll(G1) and Ll(G2) are isometrically isomorphic, then G1 and G2 are isomorphic (Wendel, 1952, [8]). There is evidence that the following generalization of Wendel's result is true.If T is an algebra isomorphism of L1(G1) onto L1(G2) with ∥T∥ < √2, then G1, and G2 are isomorphic.
The distribution of cube-full numbers
Authors: Shiu P. 
Published: May 2009

AbstractAn elementary derivation of the asymptotic formula for the number of cube-full numbers up to x is given. This derivation is used, together with an estimation of a three dimensional exponential sum, to establish the asymptotic formula for the number of cube-full numbers in the short interval x < n < x⅔+θ where 140/1123 < θ < 1/3.
On projective characters of prime degree
Authors: Higgs R. J. 
Published: May 2009

All groups G considered in this paper are finite and all representations of G are defined over the field of complex numbers. The reader unfamiliar with projective representations is referred to [9] for basic definitions and elementary results.Let Proj(G, α) denote the set of irreducible projective characters of a group G with cocycle α. In a previous paper [3] the author showed that if G is a (p, α)-group, that is the degrees of the elements of Proj(G, α) are all powers of a prime number p, then G is solvable. However Isaacs and Passman in [8] were able to give structural information about a group G for which ξ(1) divides pe for all ξ ∈ Proj(G, 1), where 1 denotes the trivial cocycle of G, and indeed classified all such groups in the case e = l. Their results rely on the fact that G has a normal abelian p-complement, which is false in general if G is a (p, α)-group; the alternating group A4 providing an easy counter-example for p = 2.
On sparsely totient numbers
Authors: Harman Glyn 
Published: May 2009

Following Masser and Shiu [6] we say that a positive integer n is sparsely totient ifHere φ is the familiar Euler totient function. We write ℱ for the set of sparsely totient numbers. In [6] several results are proved about the multiplicative structure of ℱ. If we write P(n) for the largest prime factor of n then it was shown (Theorem 2 of [6]) thatand infinitely often
Algebraic ideals of semiprime Banach algebras
Authors: Giotopoulos S. , Roumeliotis M. 
Published: May 2009

AbstractIf A is a semiprime Banach algebra, soc A, rad A the socle and radical of A, then Soc A ∩ rad A = (0). This elementary result enables us to prove some results concerning algebraic ideal and algebraic elements modulo the socle of A. We also deduce several conditions for A equivalent to the condition dim A <+∞.
Universal notions characterizing spectral decompositions
Authors: Lange Ridgley , Wang Shengwang 
Published: May 2009

In this note we characterize certain types of spectral decomposition in terms of “universal” notions valid for any operator on a Banach space. To be precise, let X be a complex Banach space and let T be a bounded linear operator on X. If F is a closed set in the plane C, let X(T, F) consist of all y ∈ X satisfying thes identitywhere f:C\F → X is analytic. It is then easy to see that X(T, F) is a T-invariant linear manifold in X. Moreover, if y ∈ X thenis a compact subset of the spectrum σ(T). Our aim is to give necessary and sufficient conditions for a decomposable or strongly decomposable operator in terms of X(T, F) and γ(y, T). Recall that T is decomposable if whenever G1G2 are open and cover C there exist T-invariant closed linear manifolds M1, M2 with X= M1 + M2 and σ(T | M1) ⊂ Gi(i = 1,2) (equivalently, σ(T | Mi)⊂ Ḡi, see [4, p. 57]). In this case, X(T, F) is norm closed if Fis closed and each y in X has a unique maximally defined local resolvent satisfying (1.1) on C\Fy; Fy is called the local spectrum σ(y, T) and coincides with γ(y, T). Hence T has the single valued extension property (SVEP); i.e., zero is the only analytic function f:V → X satisfying (z − T)f(z) = 0 on V. If T is decomposable and the restriction T | X(T, F) is also decomposable for each closed F, then T is called strongly decomposable. We point out that Albrecht [2] has shown by example that not every decomposable operator is strongly decomposable, while Eschmeier [6]has given a simpler construction to show that this phenomenon occurs even in Hilbert space.
Some isometric characterizations of ln∞
Authors: Zhu Jiang 
Published: May 2009

The previous results on isometrically characterizing ln∞ in terms of operator ideal norms can be summarized as follows.Let E be an n-dimensional Banach space.(1) If λ(E) = 1, then (see [3], [5], [6]), where λ(E) is the projection constant of E (see [4]).(2) If π(E) = n, then (see [1],[2]).(3) If Δ2(E) = √n, then (see [8]), where Δ2(E) is the 2-dominated constant of E(see [4]).(4) If for any linear operator T: → E, v1(T) = (T), then (see [7]), where v1 is the 1-nuclear norm (see [4]).
A note on the joint operator norm of hermitian operators on Banach spaces
Authors: Chō Muneo , Huruya Tadasi 
Published: May 2009

Let X be a complex Banach space and H be a hermitian operator on X. Then in [7] Sinclair proved that r(H) = ¶H¶, where r(H) and ¶H¶ are the spectral radius and the operator norm of H, respectively.For a commuting n-tuple T = (T1,…, Tn) of operators on X, we denote the (Taylor) joint spectrum of T by σ(T) (see [9]) and define the joint operator norm ¶T¶ and the joint spectral radius r(T) byandrespectively.
On a result of Johnson about Schur multipliers
Authors: Wiegold James 
Published: May 2009

The purpose of this short note is to give a new and shorter proof of the following theorem of Johnson [1], and to extend it somewhat.Theorem 1. Let G be a finite non-cyclic p-group possessing a non-empty subset X such that, for each x in X, <X/{x}>G′ is a complement for <x> in G. Then the Schur multiplier of G is non-trivial.
On the fundamental group of a Lie semigroup
Authors: Neeb Karl-Hermann 
Published: May 2009

The simplest type of Lie semigroups are closed convex cones in finite dimensional vector spaces. In general one defines a Lie semigroup to be a closed subsemigroup of a Lie group which is generated by one-parameter semigroups. If W is a closed convex cone in a vector space V, then W is convex and therefore simply connected. A similar statement for Lie semigroups is false in general. There exist generating Lie semigroups in simply connected Lie groups which are not simply connected (Example 1.15). To find criteria for cases when this is true, one has to consider the homomorphisminduced by the inclusion mapping i:S→G, where S is a generating Lie semigroup in the Lie group G. Our main results concern the description of the image and the kernel of this mapping. We show that the image is the fundamental group of the largest covering group of G, into which S lifts, and that the kernel is the fundamental group of the inverse image of 5 in the universal covering group G. To get these results we construct a universal covering semigroup S of S. If j: H(S): = S ∩ S-1 →S is the inclusion mapping of the unit group of S into S, then it turns out that the kernel of the induced mappingmay be identfied with the fundamental group of the unit group H(S)of S and that its image corresponds to the intersection H(S)0 ⋂π1(S), where π1(s) is identified with a central subgroup of S.
Some subgroups of SL(3, z) generated by involutions
Authors: Humphries Stephen P. 
Published: May 2009

For R a commutative ring with identity 1 we let SL(n, R) denote the group of n × n integral matrices with determinant 1. A transvection T is an element of SL(n, R) which we represent (see [1]) as a pair (φ d) where φ ∈ (Rn)*, the dual space of Rn, d ∈ Rn, φ(d) = 0, and for all x ∈ Rn we haveT(x) = + φ(x) d.Throughout this paper an involution is an element Y of SL(n, R) which has order two. Let n = 3 and R = Z and let C = diag(–1, –1, –1) be the central element of GL(3, Z).
On permutation polynomials whose difference is linear
Authors: Stothers W. W. 
Published: May 2009

Let q be a power of a prime p, and let Sqbe the set of permutations of {0, 1,…, q – 1). As Sq is isomorphic to the group of permutations of Fq, the field of q elements, each element of 5, can be regarded as a polynomial over Fq. Various authors (e.g. [1], [2], [3]) have considered functions f(x) such thatf(x) ∈ Sq, and (f(x) + λ×) ∈ Sqfor some λ ∈ Fq when λ = 1, f(x) is a complete mapping polynomial ([3]).
On Schachermayer's example about the Banach-Saks property
Authors: Nunez Carmelo 
Published: May 2009

A Banach space (X, ∥.∥) is said to have the Banach-Saks property (B.S.P.) if, for every bounded sequence (xn) in X, we can choose a subsequence () of (xn) such that the sequenceconverges in the X-norm. This property, that a Banach space may enjoy or not, has been extensively studied.
Conjugacy of free finite group actions on infranilmanifolds
Authors: Sadowski Michał 
Published: May 2009

In this note we give the proof of the following result (previously known for homotopically trivial and free actions on infranilmanifolds [3, Theorem 5.6]).Theorem 1. Let G be a finite group acting freely and smoothly on a closed infranilmanifold M. Assume that dim M≠3, 4. Then the action of G is topologically conjugate to an affine action.
On the location of the roots of polynomial congruences
Authors: Hooley C. 
Published: May 2009

We have indicated in our tract [9] that several interesting problems in the theory of numbers are related to results about the evenness of the distribution of the roots v of a polynomial congruencewhere f(x) = a0xn + … + an is an irreducible polynomial having integral coefficients and degree n≧2. We alluded, for example, to our work on the Chebyshev problem of the greatest prime factor of n2 – D [8], in which an essential component was our earlier demonstration [6] of the uniform distribution, modulo 1, of v/k when f(x) = x2 – D. But, having pointed out that the quantitative descriptions of such uniformity had to be very sharp for substantial applications, we then noted with regret that little more than mere uniform distribution was obtained in our generalization [7] of [6] to congruences of higher degree. Indeed, it has only been for certain cubic polynomials that results have been produced that are comparable in power with those for quadratic polynomials, and even these depend on the assumption of the unproved hypothesis R* regarding the size of incomplete Kloosterman sums [10].
Approximating Fredholm operators on a nonseparable Hilbert space
Authors: Bouldin Richard 
Published: May 2009

AbstractThis paper obtains a simple formula for the distance from a given operator to the set of invertible operators without requiring the underlying space to be separable. That formula is used to compute the distance to the Fredholm operators with a given index. These results require the further study of the concepts of essential nullity and essential deficiency, which permitted us to characterize the closure of the invertible operators. We also introduce a parameter called the modulus of Fredholmness.