2022/11/19 by Vikas Kumar, Kumar, Vikash, A. Swaminathan +1
Mathematics · #33C05 #33C45 #42C05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2211.10704
openalex publication_date 2022/11/19 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28
In this work, the concept of quasi-type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. The process of recovering orthogonality for the linear combination of a quasi-type kernel polynomial with another orthogonal polynomial, which is identified by involving linear spectral transformation, is provided. This process involves an expression of ratio of iterated kernel polynomials. This lead to considering the limiting case of ratio of kernel polynomials involving continued fractions. Special cases of such ratios in terms of certain continued fractions are exhibited.