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An Uncertainty Principle For Hankel Transforms
"... There exists a generalized Hankel transform of order ff \Gamma1=2 on R, which is based on the eigenfunctions of the Dunkl operator T ff f(x) = f 0 (x) + \Gamma ff + 1 2 \Delta f(x) \Gamma f(\Gammax) x ; f 2 C 1 (R): For ff = \Gamma1=2 this transform coincides with the usual Fourier transf ..."
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Cited by 21 (4 self)
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There exists a generalized Hankel transform of order ff \Gamma1=2 on R, which is based on the eigenfunctions of the Dunkl operator T ff f(x) = f 0 (x) + \Gamma ff + 1 2 \Delta f(x) \Gamma f(\Gammax) x ; f 2 C 1 (R): For ff = \Gamma1=2 this transform coincides with the usual Fourier transform on R. In this paper the operator T ff replaces the usual first derivative in order to obtain a sharp uncertainty principle for generalized Hankel transforms on R. It generalizes the classical WeylHeisenberg uncertainty principle for the position and momentum operators on L 2 (R); moreover, it implies a WeylHeisenberg inequality for the classical Hankel transform of arbitrary order ff \Gamma1=2 on [0; 1[:
Convolution structures and arithmetic cohomology, eprint: arXiv
 math.AG980751 v3 3
, 2001
"... This is a preliminary version of the paper. Some proofs are skipped or sketched. 1. ..."
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This is a preliminary version of the paper. Some proofs are skipped or sketched. 1.
HOMOMORPHISMS OF l1ALGEBRAS ON SIGNED POLYNOMIAL HYPERGROUPS
"... Abstract. Let {Rn} and {Pn} be two polynomial systems which induce signed polynomial hypergroup structures on N0. We investigate when the Banach algebra l1(N0, hR) can be continuously embedded into or is isomorphic to l1(N0, hP). We find sufficient conditions on the connection coefficients cnk give ..."
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Abstract. Let {Rn} and {Pn} be two polynomial systems which induce signed polynomial hypergroup structures on N0. We investigate when the Banach algebra l1(N0, hR) can be continuously embedded into or is isomorphic to l1(N0, hP). We find sufficient conditions on the connection coefficients cnk given by Rn = ∑n k=0 cnkPk, for the existence of such an embedding or isomorphism. Finally we apply these results to obtain amenabilityproperties of the l1algebras induced by BernsteinSzego ̋ and Jacobi polynomials. 1. Introduction and
Partial Characters And Signed Quotient Hypergroups
"... If G is a closed subgroup of a commutative hypergroup K; then the coset space K/G carries a natural quotient hypergroup structure. In this paper, we study related convolution structures on K=G which are obtained as deformations of the quotient hypergroup structure by certain functions on K which we ..."
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If G is a closed subgroup of a commutative hypergroup K; then the coset space K/G carries a natural quotient hypergroup structure. In this paper, we study related convolution structures on K=G which are obtained as deformations of the quotient hypergroup structure by certain functions on K which we call partial characters with respect to G . They are not probabilitypreserving and lead to socalled signed hypergroups on K/G . A first example is provided by the Laguerre convolution on [0; 1[; which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. As a further class of examples, signed hypergroups associated with the Gelfand pair (U(n,1), U(n)) are discussed.
Multidimensional Heisenberg convolutions and product formulas for multivariate Laguerre polynomials
, 2012
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An orthogonal polynomial sequence
"... Abstract. We show a weak analogon of Bochner’s theorem for polynomial hypergroups. We examine which assumptions are necessary to regain some of the statements of the original theorem. We conclude that orthogonality and nonnegativity are not crucial for the theorem. In order to show one of our result ..."
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Abstract. We show a weak analogon of Bochner’s theorem for polynomial hypergroups. We examine which assumptions are necessary to regain some of the statements of the original theorem. We conclude that orthogonality and nonnegativity are not crucial for the theorem. In order to show one of our results, we provide a polynomial inequality, which characterizes the size of the set where a real polynomial on the real line is bounded by some constant
Harmonic Analysis on Discrete Generalized Hypergroups
"... 1 Introduction Locally compact hypergroups were independently introduced around the 1970's by Dunkl [4], Jewett [9] and Spector [23]. They generalize the concepts of locally compact groups with the purpose of doing standard harmonic analysis. Similar structures had been studied earlier in the 1 ..."
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1 Introduction Locally compact hypergroups were independently introduced around the 1970's by Dunkl [4], Jewett [9] and Spector [23]. They generalize the concepts of locally compact groups with the purpose of doing standard harmonic analysis. Similar structures had been studied earlier in the 1950's by Berezansky and colleagues, and even earlier in works of Delsarte and Levitan. Later on results of harmonic analysis on hypergroups were transferred to different applications. For example a Bochner theorem is used essentially in the context of weakly stationary processes indexed by hypergroups, see [13] and [15]. Hypergroup structure is also heavily used
Revised version Contents
, 2001
"... 1. Some results from harmonic analysis 3 2. Ghostspaces and their dimensions 6 3. Short exact sequences of ghostspaces 11 ..."
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1. Some results from harmonic analysis 3 2. Ghostspaces and their dimensions 6 3. Short exact sequences of ghostspaces 11