Reduced synthesis in harmonic analysis and compact synthesis in operator theory

V. S. Shulman, I. G. Todorov, L. Turowska

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Abstract

The notion of reduced synthesis in the context of harmonic analysis on general locally compact groups is introduced; in the classical situation of commutative groups, this notion means that a function f in the Fourier algebra is annihilated by any pseudofunction supported on f −1(0). A relationship between reduced synthesis and compact synthesis (i.e., the possibility of approximating compact operators by pseudointegral ones without increasing the support) is determined, which makes it possible to obtain new results both in operator theory and in harmonic analysis. Applications to the theory of linear operator equations are also given.
Original languageEnglish
Pages (from-to)240-243
Number of pages4
JournalFunctional Analysis and Its Applications
Volume51
Issue number3
DOIs
Publication statusPublished - 01 Jul 2017

Bibliographical note

The article was accepted for publication in the first half of 2017.

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