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| Authors |
Martin Hallnäs Simon Ruijsenaars |
|---|---|
| Published in | Representation theory, special functions and Painlevé equations. RIMS 2015, Kyoto, Japan, March 3-6, 2015, s. 195-245 |
| Publisher | Mathematical Society of Japan / World Scientific Publishing |
| Publication year | 2018 |
| Published at |
Department of Mathematical Sciences |
| Language | en |
| Links |
https://doi.org/10.1142/e057 |
| Keywords | product formulas, quantum Calogero-Moser systems, conical function |
| Subject categories | Mathematical Analysis, Control Engineering, Production Engineering, Human Work Science and Ergonomics |
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.
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