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- W2951515910 abstract "We study mapping properties of operators with kernels defined via a combination of continuous and discrete orthogonal polynomials, which provide an abstract formulation of quantum (q-) Fourier type systems. We prove Ismail conjecture regarding the existence of a reproducing kernel structure behind these kernels, by establishing a link with Saitoh theory of linear transformations in Hilbert space. The results are illustrated with Fourier kernels with ultraspherical weights, their continuous q-extensions and generalizations. As a byproduct of this approach, a new class of sampling theorems is obtained, as well as Neumann type expansions in Bessel and q-Bessel functions." @default.
- W2951515910 created "2019-06-27" @default.
- W2951515910 creator A5023060610 @default.
- W2951515910 date "2006-01-09" @default.
- W2951515910 modified "2023-10-15" @default.
- W2951515910 title "The reproducing kernel structure arising from a combination of continuous and discrete orthogonal polynomials into Fourier systems" @default.
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