Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup

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We discuss the Wehrl-type entropy inequality conjecture for the group SU(1,1) and for its subgroup AX+B (or affine group), their representations on L2(R+), and their coherent states. For AX+B the Wehrl-type conjecture for Lp-norms of these coherent states (also known as the Renyi entropies) is proved in the case that p is an even integer. We also show how the general AX+B case reduces to an unsolved problem about analytic functions on the upper half-plane and the unit disk.

Keywords: Coherent states, affine group, AX+B group
Original languageEnglish
Title of host publicationPartial Differential Equations, Spectral Theory, and Mathematical Physics : The Ari Laptev Anniversary Volume
EditorsPavel Exner, Rupert Frank, Fritz Gesztesy, Helge Holden, Timo Weidl
PublisherEuropean Mathematical Society Publishing House
Publication date15 Jun 2021
ISBN (Print)978-3-98547-007-5
Publication statusPublished - 15 Jun 2021

ID: 291935414