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VOL. 76 | 2018 Product formulas for the relativistic and nonrelativistic conical functions
Martin Hallnäs, Simon Ruijsenaars

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

Abstract

The conical function and its relativistic generalization can be viewed as eigenfunctions of the reduced 2-particle Hamiltonians of the hyperbolic Calogero-Moser system and its relativistic generalization. We prove new product formulas for these functions. As a consequence, we arrive at explicit diagonalizations of integral operators that commute with the 2-particle Hamiltonians and reduced versions thereof. The kernels of the integral operators are expressed as integrals over products of the eigenfunctions and explicit weight functions. The nonrelativistic limits are controlled by invoking novel uniform limit estimates for the hyperbolic gamma function.

Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07039304
MathSciNet: MR3837923

Digital Object Identifier: 10.2969/aspm/07610195

Subjects:
Primary: 33C05, 33E30, 39A70, 47G10, 81R12

Rights: Copyright © 2018 Mathematical Society of Japan

PROCEEDINGS ARTICLE
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