Beurling-Fourier algebras on Lie groups and their spectra
Preprint, 2018

We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU(n), the Heisenberg group H, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover \tilde E(2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate "polynomially growing" weights does not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras

Author

Mahya Ghandehari

University of Delaware

Hun Hee Lee

Seoul National University

Jean Ludwig

University of Lorraine

Lyudmyla Turowska

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Nico Spronk

University of Waterloo

Subject Categories

Mathematics

Mathematical Analysis

Roots

Basic sciences

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Latest update

1/20/2020