Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis
Given a sequence of orthogonal polynomials { L n } n = 0 ∞ , orthogonal with respect to a positive Borel ν measure supported on R + , let { Q n } n = 0 ∞ be the the sequence of orthogonal polynomials with respect to the modified measure r ( x ) d ν ( x ) , where r is certain rational function. This...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/40260 |
| Acceso en línea: | https://hdl.handle.net/10115/40260 |
| Access Level: | acceso abierto |
| Palabra clave: | orthogonal polynomials asymptotic behavior rational modifications |
| Sumario: | Given a sequence of orthogonal polynomials { L n } n = 0 ∞ , orthogonal with respect to a positive Borel ν measure supported on R + , let { Q n } n = 0 ∞ be the the sequence of orthogonal polynomials with respect to the modified measure r ( x ) d ν ( x ) , where r is certain rational function. This work is devoted to the proof of the relative asymptotic formula Q n ( d ) ( z ) L n ( d ) ( z ) ⇉ n ∏ k = 1 N 1 a k + i z + a k A k ∏ j = 1 N 2 z + b j b j + i B j , on compact subsets of C ∖ R + , where a k and b j are the zeros and poles of r, and the A k , B j are their respective multiplicities |
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