Reduced synthesis in harmonic analysis and compact synthesis in operator theory

• 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.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

locally compact group

reduced C*-algebra of a locally compact group

Fourier algebra

compact operator

masa-bimodule

linear operator equation

spectral-synthesis

algebras

sets

multipliers

subspaces

Mathematics

reduced C*-algebra of a locally compact group

Publication and Content Type

ref (subject category)

art (subject category)