2022/12/22 by Yu Luo, Luo, Yu, Satoshi Tsujimoto +1
Chemistry · Decision Sciences · #33C45 #33C47 #42C05 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Scientific Measurement and Uncertainty Evaluation #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.2212.12429
openalex publication_date 2022/12/22 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
A formulation is given for the spectral transformation of the generalized eigenvalue problem through the decomposition of the second-order differential operators. This allows us to construct some Laurent biorthogonal polynomial systems with gaps in the degree of the polynomial sequence. These correspond to an exceptional-type extension of the orthogonal polynomials, as an extension of the Laurent biorthogonal polynomials. Specifically, we construct the exceptional extension of the Hendriksen-van Rossum polynomials, which are biorthogonal analogs of the classical orthogonal polynomials. Similar to the cases of exceptional extensions of classical orthogonal polynomials, both of state-deletion and state-addition occur.