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Universal symbols on locally compact Abelian groups

Content Provider	Springer Nature Link
Author	Gorin, E. A. rvidas, S.
Copyright Year	2013
Abstract	From the viewpoint of elementary functional analysis, Bernstein inequalities are mainly sharp estimates for the norms of certain operators of convolution of entire functions bounded on the real line and having finite exponential type not exceeding a given one with (complex) Borel measures of finite total variation.If we assume that the functions are defined on a locally compact Abelian group and use the uniform norms, then the generalized Bernstein spaces are parametrized by compact sets in the dual group X and the symbols of the operators are the restrictions to compact sets in X of functions locally coinciding with the Fourier transforms of measures. There exists symbols such that, in the case of uniform norms (and then, as it turns out, also in more general cases), the norm of the corresponding operator coincides with its spectral radius. The main result of the paper is a description of these (universal) symbols in terms of positive definite functions. Connected groups play a special role here.
Starting Page	1
Ending Page	13
Page Count	13
File Format	PDF
ISSN	00162663
Journal	Functional Analysis and Its Applications
Volume Number	47
Issue Number	1
e-ISSN	15738485
Language	English
Publisher	Springer US
Publisher Date	2013-03-14
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	complex Banach algebra locally compact Abelian group Bernstein inequalities positive definite function spectrum Analysis Functional Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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