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Interactions between Harmonic Analysis and Operator Theory

Todorov, I. G. — 2015

Serdica Mathematical Journal

[Todorov I. G.; Тодоров И. Г.] The artice is a survey of several topics that have led to fruitful interactions between Operator Theory and Harmonic Analysis, including operator and spectral synthesis, Schur and Herz-Schur multipliers, and reflexivity. Some open questions and directions are included in a separate section. 2010 Mathematics Subject Classification: Primary 47L05, 47L35; Secondary 43A45.

Sets of p-multiplicity in locally compact groups

I. G. Todorov;  L. Turowska — 2015

Studia Mathematica

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E * = ( s , t ) : t s - 1 ∈ E is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone-von Neumann Theorem.

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