q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators Article Swipe

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Mourad E. H. Ismail , Ruiming Zhang , Keru Zhou ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2012.07549

We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation operators. Applications include connection relations and bilinear formulas for the Askey-Wilson polynomials. We also introduce a q-Gauss-Weierstrass transform and prove a representation and inversion theorem for it.

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Mathematics

Bilinear Interpolation

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Mathematics Bilinear interpolation Gauss Pure mathematics Operator (biology) Connection (principal bundle) Askey–Wilson polynomials Representation (politics) Spectral theorem Algebra over a field Orthogonal polynomials Operator theory Wilson polynomials Jacobi polynomials Politics Repressor Physics Geometry Gene Transcription factor Quantum mechanics Chemistry Biochemistry Law Political science Statistics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2012.07549
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DOI: https://doi.org/10.48550/arxiv.2012.07549

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Title: q-Fractional Askey-Wilson Integrals and Related Semigroups of Operators

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Language: en

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Publication year: 2020

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Publication date: 2020-12-11

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Authors: Mourad E. H. Ismail, Ruiming Zhang, Keru Zhou

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Concepts: Mathematics, Bilinear interpolation, Gauss, Pure mathematics, Operator (biology), Connection (principal bundle), Askey–Wilson polynomials, Representation (politics), Spectral theorem, Algebra over a field, Orthogonal polynomials, Operator theory, Wilson polynomials, Jacobi polynomials, Politics, Repressor, Physics, Geometry, Gene, Transcription factor, Quantum mechanics, Chemistry, Biochemistry, Law, Political science, Statistics

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