Recovering orthogonality from quasi-nature of Spectral transformations

Autor:	Kumar, Vikash, Marcellán, Francisco, Swaminathan, A.
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs 42C05 33C45 26C10 11A55
Druh dokumentu:	Working Paper
Popis:	In this contribution, quasi-orthogonality of polynomials generated by Geronimus and Uvarov transformations is analyzed. An attempt is made to discuss the recovery of the source orthogonal polynomial from the quasi-Geronimus and quasi-Uvarov polynomials of order one. Moreover, the discussion on the difference equation satisfied by quasi-Geronimus and quasi-Uvarov polynomials is presented. Furthermore, the orthogonality of quasi-Geronimus and quasi-Uvarov polynomials is achieved through the reduction of the degree of coefficients in the difference equation. During this procedure, alternative representations of the parameters responsible for achieving orthogonality are derived. One of these representations involves the Stieltjes transform of the measure. Finally, the recurrence coefficients ensuring the existence of a measure that makes the quasi-Geronimus Laguerre polynomial of order one an orthogonal polynomial are calculated. Comment: 26 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.03789 Zobrazit plný text záznamu View this record from Arxiv