摘要:

AbstractWe prove the strong law of large numbers for logarithmic averages of random vectors. We also obtain a strong approximation for logarithmic averages.

ISSN:0025-584X    

DOI:10.1002/mana.19981950102

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe study the eigenvalue behaviour of a class of ODE acting on the semiaxis. Using interpolation of quasinormed spaces as one of our main tools, we obtain sharp estimates of the counting function of eigenvaluesn(λ). In particular, some of our results become reversible if a matrix‐valued “weight” ‐function is nonnegative. The asymptotic behaviour ofn(λ) is also

ISSN:0025-584X    

DOI:10.1002/mana.19981950103

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19981950104

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractLet Ω be an irreducible Cartan domain of rankrand genuspandBv(c>p‐ 1) be the Berezin transform on Ω. It is known that asvtends to infinity, the Berezin transform admits the asymptotic expansionBν∼∑k=0∞Qkν−kwhere theQk's are certain invariant differential operators — for instance,Q0is the identity andQ1is the Laplace ‐ Beltrami operator. [See A. Unterberger and H. Upmeier, Comm. Math. Phys.164(1994), 563–598.] In the present paper we show that the operatorsQkgenerate the whole ring of invariant differential operators on Ω; in fact,Q1,Q3,…,Q2r‐1andQ0form a set of free generators. A bounded version of this result is also given: for anyv>p‐ 1, ther+1 operatorsBv,Bv+1,…,Bv+rare a set of generators for the von Neumann algebra 3 of allG‐ invariant bounded linear operators onL2(Ω); this algebra can be identified with the algebra of allL2‐ bounded Fourier multipliers, or of all bounded operators which are functions, in theL2‐ spectral‐theoretic sense, of certain normal extensions of

ISSN:0025-584X    

DOI:10.1002/mana.19981950105

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractUsing Lyapunov functionals the global behaviour of the solutions of a reaction‐diffusion system modelling chemotaxis is studied for bounded piecewise smooth domains in the plane. Geometric criteria can be given so that this dynamical system tends to a (not necessarily trivial) stationary stat

ISSN:0025-584X    

DOI:10.1002/mana.19981950106

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractLetSbe a closed symmetric operator with defect numbers (1,1) in a Hilbert space

ISSN:0025-584X    

DOI:10.1002/mana.19981950107

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractLet us denote byCr(K, ·),r∈ {0,…,d‐ 1}, the curvature measures of a convex bodyKin the Euclidean spaceℝdwithd≥ 2. According to Lebesgue's decomposition theorem the curvature measure of orderrofK, Cr(K, ·), can be written as the sum of an absolutely continuous measure,Car(K, ·), and a singular measure,Csr(K, ·), with respect to (d‐ 1) ‐ dimensional Hausdorff measure. For example, ifKis a polytope, thenCar(K, ·) = 0 and ifKis sufficiently smooth, thenCsr(K, ·) = 0. For a general convex bodyK, a description ofCar(K, ·) in terms of geometric quantities is known. In the present paper, we provide a corresponding explicit representation for the singular partCsr(K, .). Further, denote by Σr(K) the set ofr‐singular boundary points of the convex bodyK·It is known that Σr(K) has σ‐finite, but possibly infinite,r‐ dimensional Hausdorff measure. Provided that the singular partCsr(K, ·) of the curvature measure of orderrvanishes, for a given convex bodyK, we prove that ther‐ dimensional Hausdorff measure of Σr(K) also vanishes. Examples show that in a certain sense this result is sharp. Analogous results are established for surface area me

ISSN:0025-584X    

DOI:10.1002/mana.19981950108

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractGiven twoQ‐ functionsfandg, a symmetric relation and a selfadjoint extension is constructed whoseQ‐ function is the compositionfog.To obtain this result we use the concept of tensor products of Hilbert spaces. Furthermore for a symmetric relationSand a selfadjoint extensionAtheQ‐ function ofSandAis related to theQ‐ function ofS−1andA−1. This connection is used to characterize some properties ofSandAby means of their

ISSN:0025-584X    

DOI:10.1002/mana.19981950109

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractWe construct infinite class field towers of global function fields with asymptotically many rational places. In this way, we improve on asymptotic bounds of Serre, Perret, Schoof, and Xing. The results can be interpreted equivalently as asymptotic bounds on the number of rational points of smooth algebraic curves over finite fields. As an application, we show an improvement on the Gilbert‐Varshamov bound for linear codes over finite fields of a sufficiently large composite nonsquare orde

ISSN:0025-584X    

DOI:10.1002/mana.19981950110

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY

摘要:

AbstractLet (Mr)r∈ℕ0be a logarithmically convex sequence of positive numbers which verifiesM0= 1 as well asMr≥ 1 for everyr∈ ℕ and defines a non quasi ‐ analytic class. Let moreoverFbe a closed proper subset of ℝn. Then for every functionfon ℝnbelonging to the non quasi ‐ analytic (Mr)‐class of Beurling type, there is an elementgof the same class which is analytic on ℝ,nFand such that Dαf(x) = Dαg(x)

ISSN:0025-584X    

DOI:10.1002/mana.19981950111

出版商:WILEY‐VCH Verlag    

年代:1998

数据来源: WILEY