Geodesic
Reduced synthesis in harmonic analysis and compact synthesis in operator theory
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 98-102

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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.
Keywords: locally compact group, reduced $C^*$-algebra of a locally compact group, Fourier algebra compact operator, linear operator equation.
Mots-clés : masa-bimodule 
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     title = {Reduced synthesis in harmonic analysis and compact synthesis in operator theory},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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I. G. Todorov; L. Turowska; V. S. Shulman. Reduced synthesis in harmonic analysis and compact synthesis in operator theory. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 98-102. http://geodesic.mathdoc.fr/item/FAA_2017_51_3_a8/