Scattering Theory of Discrete (Pseudo) Laplacians on a Weyl Chamber
To a crystallographic root system we associate a system of multivariate orthogonal polynomials diagonalizing an integrable system of discrete pseudo Laplacians on the Weyl chamber. We develop the time-dependent scattering theory for these discrete pseudo Laplacians and determine the corresponding wa...
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| Veröffentlicht in: | American journal of mathematics 2005-04, Vol.127 (2), p.421-458 |
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| container_end_page | 458 |
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| container_issue | 2 |
| container_start_page | 421 |
| container_title | American journal of mathematics |
| container_volume | 127 |
| creator | Van Diejen, J. F. |
| description | To a crystallographic root system we associate a system of multivariate orthogonal polynomials diagonalizing an integrable system of discrete pseudo Laplacians on the Weyl chamber. We develop the time-dependent scattering theory for these discrete pseudo Laplacians and determine the corresponding wave operators and scattering operators in closed form. As an application, we describe the scattering behavior of certain hyperbolic Ruijsenaars-Schneider type lattice Calogero-Moser models associated with the Macdonald polynomials. |
| doi_str_mv | 10.1353/ajm.2005.0012 |
| format | Article |
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| ispartof | American journal of mathematics, 2005-04, Vol.127 (2), p.421-458 |
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| language | eng |
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| source | Jstor Complete Legacy; Project MUSE - Premium Collection; JSTOR Mathematics & Statistics |
| subjects | Algebra Calculus Classical and quantum physics: mechanics and fields Exact sciences and technology General theory of scattering Hilbert spaces Laplacians Mathematical analysis Mathematics Nonlinear equations Operator theory Physics Polynomials Recurrence relations Root systems Sciences and techniques of general use Special functions Wave functions Wave packets Weighting functions |
| title | Scattering Theory of Discrete (Pseudo) Laplacians on a Weyl Chamber |
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