Reduced synthesis in harmonic analysis and compact synthesis in operator theory
Journal article, 2017

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.

reduced C*-algebra of a locally compact group

compact operator


linear operator equation

Fourier algebra

locally compact group


Victor Shulman

Vologda State University

I. G. Todorov

Queen's University Belfast

Lyudmyla Turowska

University of Gothenburg

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Functional Analysis and its Applications

0016-2663 (ISSN) 1573-8485 (eISSN)

Vol. 51 3 240-243

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