On Bochner-Krall orthogonal polynomial systems
| dc.creator | Bergkvist, T. | |
| dc.creator | Rullgard, H. | |
| dc.creator | Shapiro, B. | |
| dc.date | 2002-09-06 | |
| dc.date.accessioned | 2026-07-07T04:50:39Z | |
| dc.date.available | 2026-07-07T04:50:39Z | |
| dc.description | In this paper we address the classical question going back to S. Bochner and H.L. Krall to describe all systems {p_{n}(x)} of orthogonal polynomials (OPS) which are the eigenfunctions of some finite order differential operator, i.e. satisfy the equation \sum_{k=1}^{N}a_{k}(x)y^{(k)}(x)=\la_{n} y(x) (1). Such systems of orthogonal polynomials are called Bochner-Krall OPS (or BKS for short) and their spectral differential operators are accordingly called Bochner-Krall operators (or BK-operators for short). We say that a BKS has compact type if it is orthogonal with respect to a compactly supported positive measure on the real line. It is well-known that the order N of any BK-operator should be even and every coefficient a_{k}(x) must be a polynomial of degree at most k. Below we show that the leading coefficient of a compact type BK-operator is of the form ((x - a)(x-b))^{N/2}. This settles the special case of the general conjecture of describing the leading terms of all BK-operators. New results on the asymptotic distribution of zeros of polynomial eigenfunctions for a spectral problem (1) are the main ingredient in the proofs. | |
| dc.description | AMSTEX, 5 pages, no pictures | |
| dc.identifier | https://arxiv.org/abs/math/0209064 | |
| dc.identifier | http://arxiv.org/abs/math/0209064 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64868 | |
| dc.subject | Spectral Theory | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | On Bochner-Krall orthogonal polynomial systems | |
| dc.type | text |