Orthogonal polynomials with discontinuous weights
| dc.creator | Chen, Yang | |
| dc.creator | Pruessner, Gunnar | |
| dc.date | 2005-01-22 | |
| dc.date.accessioned | 2026-07-07T04:31:50Z | |
| dc.date.available | 2026-07-07T04:31:50Z | |
| dc.description | In this paper we present a brief description of a ladder operator formalism applied to orthogonal polynomials with discontinuous weights. The two coefficient functions, A_n(z) and B_n(z), appearing in the ladder operators satisfy the two fundamental compatibility conditions previously derived for smooth weights. If the weight is a product of an absolutely continuous reference weight w_0 and a standard jump function, then A_n(z) and B_n(z) have apparent simple poles at these jumps. We exemplify the approach by taking w_0 to be the Hermite weight. For this simpler case we derive, without using the compatibility conditions, a pair of difference equations satisfied by the diagonal and off-diagonal recurrence coefficients for a fixed location of the jump. We also derive a pair of Toda evolution equations for the recurrence coefficients which, when combined with the difference equations, yields a particular Painleve IV. | |
| dc.description | 9 pages, 2 figures, JPA style | |
| dc.identifier | https://arxiv.org/abs/math-ph/0501057 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0501057 | |
| dc.identifier | J. Phys. A: Math. Gen. 38 (12), L191--L198 (2005) | |
| dc.identifier | doi:10.1088/0305-4470/38/12/L01 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57964 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | Orthogonal polynomials with discontinuous weights | |
| dc.type | text |