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- W4221139103 abstract "Assume that ${a_{n};,ngeq0}$ is a sequence of positive numbers and $sum a_{n}^{,-1}<infty$. Let $alpha_{n}=ka_{n}$, $beta_{n}=a_{n}+k^{2}a_{n-1}$ where $kin(0,1)$ is a parameter, and let ${P_{n}(x)}$ be an orthonormal polynomial sequence defined by the three-term recurrence [ alpha_{0}P_{1}(x)+(beta_{0}-x)P_{0}(x)=0, alpha_{n}P_{n+1}(x)+(beta_{n}-x)P_{n}(x)+alpha_{n-1}P_{n-1}(x)=0 ] for $ngeq1$, with $P_{0}(x)=1$. Let $J$ be the corresponding Jacobi (tridiagonal) matrix, i.e. $J_{n,n}=beta_{n}$, $J_{n,n+1}=J_{n+1,n}=alpha_{n}$ for $ngeq0$. Then $J^{-1}$ exists and belongs to the trace class. We derive an explicit formula for $P_{n}(x)$ as well as for the characteristic function of $J$ and describe the orthogonality measure for the polynomial sequence. As a particular case, the modified $q$-Laguerre polynomials are introduced and studied." @default.
- W4221139103 created "2022-04-03" @default.
- W4221139103 creator A5038290717 @default.
- W4221139103 date "2022-03-10" @default.
- W4221139103 modified "2023-09-27" @default.
- W4221139103 title "A family of orthogonal polynomials corresponding to Jacobi matrices with a trace class inverse" @default.
- W4221139103 doi "https://doi.org/10.48550/arxiv.2203.05350" @default.
- W4221139103 hasPublicationYear "2022" @default.
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