WKB approximation and Krall-Type orthogonal polynomials

We give an uni ed approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one \perturbed" by the addition of one or more delta Dirac functions. Some examples studied by di erent authors are considered from an unique point of vi...

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Detalles Bibliográficos
Autores: Álvarez Nodarse, Renato, Marcellán Español, Francisco, Soares Petronilho, José Carlos
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:1998
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41698
Acceso en línea:http://hdl.handle.net/11441/41698
https://doi.org/10.1023/A:1006006519197
Access Level:acceso abierto
Palabra clave:Orthogonal polynomials
Krall polynomials
WKB Approximation
tridiagonal matrices
distribution of zeros
Descripción
Sumario:We give an uni ed approach to the Krall-type polynomials orthogonal with respect to a positive measure consisting of an absolutely continuous one \perturbed" by the addition of one or more delta Dirac functions. Some examples studied by di erent authors are considered from an unique point of view. Also some properties of the Krall polynomials are studied. The three-term recurrence relation is calculated explicitly, as well as some asymptotic formulas. With special emphasis will be considered the second order di erential equations that such polynomials satisfy which allows us to obtain the central moments and the WKB approximation of the distribution of zeros. Some examples coming from quadratic transformation polynomial mappings and tridiagonal periodic matrices are also studied.