Hallnäs, M and Ruijsenaars, S (2018) Product formulas for the relativistic and nonrelativistic conical functions. In: Konno, H, Sakai, H, Shiraishi, J, Suzuki, T and Yamada, Y, (eds.) Advanced Studies in Pure Mathematics, 76. RIMS 2015: Representation Theory, Special Functions and Painlevé Equations, 03-06 Mar 2015, Kyoto University, Japan. Mathematical Society of Japan , pp. 195-246. ISBN 978-4-86497-050-1
Abstract
The conical function and its relativistic generalization can be viewed as eigen-functions 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 oper-ators 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.
Metadata
Item Type: | Proceedings Paper |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Aug 2016 09:42 |
Last Modified: | 11 Jun 2019 14:19 |
Status: | Published |
Publisher: | Mathematical Society of Japan |
Identification Number: | 10.1142/e057 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103813 |