摘要:

AbstractWe characterize the precompact sets in spaces of vector valued continuous functions and use the resulting criteria to investigate asymptotic behaviour of such functions defined on a halfline. This problem arose in the context of a qualitative study of solutions to the abstract Cauchy problem. We give particular consideration to the relationship between vector valued asymptotically almost periodic functions on a subinterval [α, ∞] of the real line and precompactness of the set of its translates. Our compactness criteria are also applied to a question concerning the approximation property for spaces of vector valued continuous functions with topologies induced by weighted analogues of the supremum norm. as well as to obtain nonlinear variants on factorization of compact operators through reflexive Banach spac

ISSN:0025-584X    

DOI:10.1002/mana.19881350102

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

摘要:

AbstractLet τ be a monotone premeasure on a certain paving ϱ of a metric space (X,d) which is supadditive for metrically separated sets of ϱ. The outer measure μIof type I as defined in Rogers book [5] by τ is a metric outer measure and agrees with the metric outer measure μIIo

ISSN:0025-584X    

DOI:10.1002/mana.19881350103

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19881350104

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19881350105

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

摘要:

AbstractLetPkc(G) denote the set of continuous functions withknegative squares on a locally compact commutative groupG.Every functionfϵPkc(G) is definitizable in the sense thatis positive definite for certain complex measures ω onGwith finite support [9]. The proof of this fact was base on a result of M. A. Naimark about common nonpositive eigenvectors of commuting unitary operators in a Pontrjagin space. It is the aim of this note to prove without any use of the theory of Pontrjagin spaces the definitizability of functionsfϵPkc(G) which are of polynomial growth. In Section 3 we show, how the definitizability of functionsfϵPkc(G) can be used to prove the existence of common non‐positive eigenvectors of commuting unitary operators in a Pontrjagin

ISSN:0025-584X    

DOI:10.1002/mana.19881350106

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19881350107

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

摘要:

AbstractLetY1,Y2,… be a sequence of random variables and letMnbe the floating‐point mantissa ofYn.Further let 11,x)(·) denote the indicator of the interval (1,x). IfYn/n→Za.s., whereZ≠ 0 is a further random variable, then the sequence 1(1,x)(Mn) converges a.s. to logxin the sense of

ISSN:0025-584X    

DOI:10.1002/mana.19881350108

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19881350109

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

摘要:

AbstractFor finite difference schemes of compact form on nonuniform grids approximatingm‐th order two‐point boundary value problems stability inequalities are proved which use a norm analogous to the Spijker‐norm in the case of multistep methods. The results are applied to a number of finite difference schemes for which they establish a higher order of convergence than naively exp

ISSN:0025-584X    

DOI:10.1002/mana.19881350110

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19881350111

出版商:WILEY‐VCH Verlag    

年代:1988

数据来源: WILEY