Reduced synthesis in harmonic analysis and compact synthesis in operator theory
Artikel i vetenskaplig tidskrift, 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.

linear operator equation

compact operator

locally compact group

Fourier algebra

reduced C*-algebra of a locally compact group



Victor Shulman

Vologda State University

I. G. Todorov

Queen's University Belfast

Lyudmyla Turowska

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Göteborgs universitet

Functional Analysis and its Applications

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

Vol. 51 240-243