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

Elliott Lieb; Jan Philip Solovej

doi:10.4171/ECR/18-1/18

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

Elliott Lieb, Jan Philip Solovej

Department of Mathematical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Abstract

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 language	English
Title of host publication	Partial Differential Equations, Spectral Theory, and Mathematical Physics : The Ari Laptev Anniversary Volume
Editors	Pavel Exner, Rupert Frank, Fritz Gesztesy, Helge Holden, Timo Weidl
Publisher	European Mathematical Society Publishing House
Publication date	15 Jun 2021
Pages	301-314
ISBN (Print)	978-3-98547-007-5
DOIs	https://doi.org/10.4171/ECR/18-1/18
Publication status	Published - 15 Jun 2021

Access to Document

10.4171/ECR/18-1/18

Cite this

Lieb, E., & Solovej, J. P. (2021). Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup. In P. Exner, R. Frank, F. Gesztesy, H. Holden, & T. Weidl (Eds.), Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume (pp. 301-314). European Mathematical Society Publishing House. https://doi.org/10.4171/ECR/18-1/18

Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup. / Lieb, Elliott; Solovej, Jan Philip.

Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume. ed. / Pavel Exner; Rupert Frank; Fritz Gesztesy; Helge Holden; Timo Weidl. European Mathematical Society Publishing House, 2021. p. 301-314.

Research output: Chapter in Book/Report/Conference proceeding › Book chapter › Research › peer-review

Lieb, E & Solovej, JP 2021, Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup. in P Exner, R Frank, F Gesztesy, H Holden & T Weidl (eds), Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume. European Mathematical Society Publishing House, pp. 301-314. https://doi.org/10.4171/ECR/18-1/18

Lieb E, Solovej JP. Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup. In Exner P, Frank R, Gesztesy F, Holden H, Weidl T, editors, Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume. European Mathematical Society Publishing House. 2021. p. 301-314 https://doi.org/10.4171/ECR/18-1/18

Lieb, Elliott ; Solovej, Jan Philip. / Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup. Partial Differential Equations, Spectral Theory, and Mathematical Physics: The Ari Laptev Anniversary Volume. editor / Pavel Exner ; Rupert Frank ; Fritz Gesztesy ; Helge Holden ; Timo Weidl. European Mathematical Society Publishing House, 2021. pp. 301-314

@inbook{2c892ed8331d4f7694c8e619eee19369,

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

abstract = "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",

author = "Elliott Lieb and Solovej, {Jan Philip}",

year = "2021",

month = jun,

day = "15",

doi = "10.4171/ECR/18-1/18",

language = "English",

isbn = "978-3-98547-007-5",

pages = "301--314",

editor = "Pavel Exner and Rupert Frank and Fritz Gesztesy and Helge Holden and Timo Weidl",

booktitle = "Partial Differential Equations, Spectral Theory, and Mathematical Physics",

publisher = "European Mathematical Society Publishing House",

address = "Switzerland",

}

TY - CHAP

T1 - Wehrl-type coherent state entropy inequalities for SU (1,1) and its AX + B subgroup

AU - Lieb, Elliott

AU - Solovej, Jan Philip

PY - 2021/6/15

Y1 - 2021/6/15

N2 - 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

AB - 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

U2 - 10.4171/ECR/18-1/18

DO - 10.4171/ECR/18-1/18

M3 - Book chapter

SN - 978-3-98547-007-5

SP - 301

EP - 314

BT - Partial Differential Equations, Spectral Theory, and Mathematical Physics

A2 - Exner, Pavel

A2 - Frank, Rupert

A2 - Gesztesy, Fritz

A2 - Holden, Helge

A2 - Weidl, Timo

PB - European Mathematical Society Publishing House

ER -