Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Copyright policy )Harmonic Analysis on Quantum Complex Hyperbolic Spaces
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.
harmonic analysis on quantum symmetric spaces, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), quantum groups, Plancherel formula, 17B37, 20G42, 81R50, 33D45, 42C10, Quantum groups (quantized enveloping algebras) and related deformations, Homogeneous complex manifolds, Functional Analysis (math.FA), Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Functional Analysis, Al-Salam-Chihara polynomials, Mathematics - Quantum Algebra, QA1-939, FOS: Mathematics, \(q\)-difference operators, Quantum Algebra (math.QA), Representation Theory (math.RT), Mathematics, Mathematics - Representation Theory, q-difference operators
harmonic analysis on quantum symmetric spaces, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), quantum groups, Plancherel formula, 17B37, 20G42, 81R50, 33D45, 42C10, Quantum groups (quantized enveloping algebras) and related deformations, Homogeneous complex manifolds, Functional Analysis (math.FA), Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), Mathematics - Functional Analysis, Al-Salam-Chihara polynomials, Mathematics - Quantum Algebra, QA1-939, FOS: Mathematics, \(q\)-difference operators, Quantum Algebra (math.QA), Representation Theory (math.RT), Mathematics, Mathematics - Representation Theory, q-difference operators
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