Asymptotic for Orthogonal Polynomials with Respect to a Rational Modification of a Measure Supported on the Semi-Axis

Carlos Féliz-Sánchez, Héctor Pijeira-Cabrera () and Javier Quintero-Roba
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Carlos Féliz-Sánchez: Instituto de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Santo Domingo, Av. Alma Mater, Santo Domingo 10105, Dominican Republic
Héctor Pijeira-Cabrera: Departamento de Matemáticas, Universidad Carlos III de Madrid, Av. de la Universidad, 30, 28911 Leganés, Spain
Javier Quintero-Roba: Departamento de Teoría de la Señal y Comunicaciones y Sistemas Telemáticos y Computación, Universidad Rey Juan Carlos, 28942 Fuenlabrada, Spain

Mathematics, 2024, vol. 12, issue 7, 1-16

Abstract: 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.

Keywords: orthogonal polynomials; asymptotic behavior; rational modifications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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