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- W4286784815 abstract "Let ${hat{P}_{n}(x)}$ be an orthonormal polynomial sequence and denote by ${w_{n}(x)}$ the respective sequence of functions of the second kind. Suppose the Hamburger moment problem for ${hat{P}_{n}(x)}$ is determinate and denote by $J$ the corresponding Jacobi matrix operator on $ell^{2}$. We show that if $J$ is positive definite and $J^{-1}$ belongs to the trace class then the series on the right-hand side of the defining equation [ mathfrak{F}(z):=1-zsum_{n=0}^{infty}w_{n}(0)hat{P}_{n}(z) ] converges locally uniformly on $mathbb{C}$ and it holds true that $mathfrak{F}(z)=prod_{n=1}^{infty}(1-z/lambda_{n})$ where ${lambda_{n};,n=1,2,3,ldots}=mathrm{Spec},J$. Furthermore, the Al-Salam-Carlitz II polynomials are treated as an example of orthogonal polynomials to which this theorem can be applied." @default.
- W4286784815 created "2022-07-24" @default.
- W4286784815 creator A5038290717 @default.
- W4286784815 date "2019-04-30" @default.
- W4286784815 modified "2023-09-27" @default.
- W4286784815 title "On infinite Jacobi matrices with a trace class resolvent" @default.
- W4286784815 doi "https://doi.org/10.48550/arxiv.1904.13199" @default.
- W4286784815 hasPublicationYear "2019" @default.
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