Almost periodic compactifications of group extensions

Let and be groups and let be an extension of by . Given a property of group compactifications, one can ask whether there exist compactifications and of N and K such that the universal -compactification of G is canonically isomorphic to an extension of by . We prove a theorem which gives necessary and sufficient conditions for this to occur for general properties and then apply this result to the almost periodic and weakly almost periodic compactifications of G.     

Majorants and Extreme Points of Unit Balls in Bernstein Spaces

The Bernstein space B ^p () (1 $$ " align="middle" border="0"> 0) is the set of functions from L ^p( ) having Fourier transforms (in the sense of generalized functions) with supports in the compact segment [- , ]. Every function f has an analytic continuation onto the complex plane, which is an entire function of exponential type . The spaces B ^p ()\, are conjugate Banach spaces. Therefore, the closed unit ball in B ^p () has a rich set of extreme (boundary) points: coincides with the weakly ^* closed convex hull of its extreme points. Since, for 1< p< , B ^p () is a uniformly convex space, only the balls and have nontrivially arranged sets of extreme points. In this paper, in terms of zeros of entire functions, we obtain necessary and sufficient conditions of extremeness for functions from .     

Spin Models and Strongly Hyper-Self-Dual Bose-Mesner Algebras

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let and denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of with respect to p. By a hyper-duality of , we mean an automorphism of such that for all ; and is a duality of . is said to be hyper-self-dual whenever there exists a hyper-duality of . We say that is strongly hyper-self-dual whenever there exists a hyper-duality of which can be expressed as conjugation by an invertible element of . We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra.     

Ideals of the semigroup of ultrafilters of a topological group

We construct two new series of closed left ideals of the semigroup of ultrafilters of a topological group (G, ). The first series gives a disjunctive decomposition of -absorbing ultrafilters. Under certain restrictions on the topology of the group (G, ), the second series gives a disjunctive decomposition of the semigroup of free ultrafilters. For a nondiscrete metrizable topological group (G, ), we construct a large free subsemigroup of the semigroup .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 4, pp. 506–511, April, 1995.     

Realizing representations on generalized flag manifolds

Let G be a complex reductive linear algebraic group and a real form. Suppose P is a parabolic subgroup of G and assume that P has a Levi factor L such that is a real form of L.Using the minimal globalization V _min of a finite length admissible representation for L ₀, one can define a homogeneous analytic vector bundle on the G ₀ orbit S of P in the generalized flag manifold . Let denote the corresponding sheaf of polarized sections. In this article we analyze the G ₀ representations obtained on the compactly supported sheaf cohomology groups .     

Some topological properties of ω-covering sets

We prove the following theorems:1. There exists an -covering with the property s ₀.2. Under cov there exists X such that is not an -covering orX \ B is not an -covering].3. Also we characterize the property of being an -covering.     

Operator inequalities and construction of Krein spaces

Let be a Hilbert space. A continuous positive operatorT on uniquely determines a Hilbert space which is continuously imbedded in and for which with the canonical imbedding . A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space ( ) which is continuously imbedded in and for which with the canonical imbedding .     

Levi Classes Generated by Nilpotent Groups

Let be a class of all groups G for which the normal closure (x) ^G of every element x belongs to a class . is a Levi class generated by . Let and ₀ be classes of finitely generated nilpotent groups and of torsion-free, finitely generated, nilpotent groups, respectively. We prove that and , and so and . It is shown that quasivarieties and are closed under free products, and that each contains at most one maximal proper subquasivariety. It is also proved that is closed under free products if so is .     

On sequences of Dirichlet polynomials uniformly bounded on half planes

Given and a sequence of Dirichlet polynomials estimates for the coefficientsa _n are proved if {_n} is uniformly bounded on a region containing a half plane. Thereby a result is obtained which is an analogue of a known result for polynomials, that is for theA-transforms of the geometric sequence; moreover a Jentzsch type theorem for {_n(z)} is derived.     

Über die Riemannsche Einbettungsgeometrie der Veronesemannigfaltigkeiten

Let E be a n-dimensional euclidean vector space. The subset V _k ⁿ ={x ... x | x E} of ^kE is called a Veronesemanifold. The scalar product of E induces a euclidean structure on ^kE. Passing to the corresponding projective space , one may consider as a riemannian submanifold of the space form . In this paper we study properties of the pair of riemannian manifolds.     

On the Spectrum of Cartesian Powers of Classical Automorphisms

We prove the following statement: the set of all essential spectral multiplicities of (n times) is on for Chacon transformations T, or, equivalently, the operator T(ⁿ) has a simple spectrum on the subspace C _Sim of all functions that are invariant with respect to permutations of the coordinates. As an immediate consequence of this fact, we have the disjointness of all convolution powers of the spectral measure for Chacon transformations. If n=2, then T× T has a homogeneous spectrum of multiplicity 2 on , i.e., this is a solution of Rokhlin's problem for Chacon transformations. Similar statements are considered for other classical automorphisms.     

Nonnegative Hall Polynomials

The number of subgroups of type and cotype in a finite abelian p-group of type is a polynomialg with integral coefficients. We prove g has nonnegative coefficients for all partitions and if and only if no two parts of differ by more than one. Necessity follows from a few simple facts about Hall-Littlewood symmetric functions; sufficiency relies on properties of certain order-preserving surjections that associate to each subgroup a vector dominated componentwise by . The nonzero components of (H) are the parts of , the type of H; if no two parts of differ by more than one, the nonzero components of – (H) are the parts of , the cotype of H. In fact, we provide an order-theoretic characterization of those isomorphism types of finite abelian p-groups all of whose Hall polynomials have nonnegative coefficients.     

über Wurzeln und Logarithmen beschrÄnkter Ma\e

Ohne ZusammenfassungBezeichnungen und Symbole G lokalkompakte topologische Gruppe - M(G)/R(G)/P(G)/ regulÄre komplexe/reelle/positive Ma\e/ - Q(G)/W(G) Ma\e mit · l/Wahrscheinlichkeitsma\e - _x Punktma\: _x(f)=f(x) - v Faltung, — Bekanntlich bildet M(G) bezüglich der Faltung eine Banachalgebra; - Involution in M(G), , wobei — die Komplexkonjugierte bezeichnet - × diskreter Anteil eines Ma\es, - T _gm Faltungsoperator auf L ² (G) (bezüglich des linken Haarschen Ma\es), f.ü. - p(·)/q(·)/u(·) - exp(·.) Exponentialfunktion, exp - normal/unitÄr/symmetrisch/positiv definit bezeichnet man ein Ma\ , wenn der Faltungsoperator T diese Eigenschaft besitzt - invertierbar hei\t M(G), wenn ein vM(G) existiert, so da\ v = v= _e - _1/n n-te Wurzel von ₁ hei\t wenn( _1/n)ⁿ= ₁ - ₁ hei\t unendlich teilbar wenn zu jedem natürlichen n eine n-te Wurzel _1/n von existiert - N Menge der natürlichen Zahlen     

A Characterisation of the Generalized Quadrangle Q (5, q) Using Cohomology

If a GQ S of order (s, s) is contained in a GQ S of order (s, s ²) as a subquadrangle, then for each point X of S\S the set of points of S collinear with X form an ovoid of S. Thas and Payne proved that if S= (4,q),q even, and is an elliptic quadric for each XS\S,thenS (5,q). In this paper we provide a single proof for the q odd and q even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex.     

The type set for some measures on \mathbb{R}^{2n} with n-dimensional support

Let be realhomogeneous functions in ofdegree and let bethe Borel measure on given by

Boundedness in the mean of orthonormalized polynomials

For the polynomials {p_n(t)} ₀ , orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t) _v=1 ^m , we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1) 2) and 3) with the conditions that on [–1, 1] and (H,)^–1 L²(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973.     

On the Characterisation of AG(n,q) by its Parameters asa Nearly Triply Regular Design

We show that a non-symmetric nearly triply regular designD with and in which every line has at least q points is AG(n,q) for prime power q > 2 and positiveinteger n 3.     

Isometric dilations in nest algebras

LetT be a contraction acting in a separable Hilbert space and leaving invariant a nest of subspaces of . We answer the question: when doesT have an isometric extension to which leaves invariant the nest = {N N :N ;}.     

Fonctions Séparément Finement Surharmoniques

Nous montrons que toute fonction séparément finement surharmonique sur un ouvert de la topologie produit _{n_1}×s× _{n_k} des topologies fines des espaces R ⁿ ₁,. . ., R ⁿ _k, _{n_1}×s× _{n_k}-localement bornée inférieurement est finement surharmonique dans . On en déduit que toute fonction séparément finement harmonique, _{n_1}×s× _{n_k}-localement bornée sur est finement harmonique dans .Separately Finely Superharmonic Functions Abstract.We prove that every separately finely surperharmonic function on an open set in R ⁿ ₁×s×R ⁿ _k for the product _{n_1}×s× _{n_k} of the fine topologies on the spaces R ⁿ ₁,. . ., R ⁿ _k, _{n_1}×s× _n-_klocally lower bounded, is finely superharmonic in . We then deduce that every separateltly finely harmonic function _{n_1}×s× _{n k}-locally bounded in is finely harmonic.