After Plancherel formula

Abstract

We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation of non-uniform spectra. Our purpose is to indicate some non-solved problems of non-commutative harmonic analysis that definitely are solvable. This is a sketch of my talks on VI School "Geometry and Physics", Bialowieza, Poland, June 2017.

11p

References in corpus (3)

• Restriction of representations of $GL(n+1,C)$ to $GL(n,C)$ and action of the Lie overalgebra
• The Fourier transform on the group $G{L}_2(R)$ and the action of the overalgebra $g{l}_4$
• Projectors separating spectra for $L^2$ on symmetric spaces $GL(n,\C)/GL(n,\R)$

Cited by in corpus (1)

• Operational calculus for Fourier transform on the group $GL(2,R)$