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Reiter’s condition P1 and approximate identities for polynomial hypergroups
 Monatsh. Math
"... Abstract. Let K be a commutative hypergroup with the Haar measure . In the present paper we investigate whether the maximal ideals in L1ðK; Þ have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals o ..."
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Abstract. Let K be a commutative hypergroup with the Haar measure . In the present paper we investigate whether the maximal ideals in L1ðK; Þ have bounded approximate identities. We will show that the existence of a bounded approximate identity is equivalent to the existence of certain functionals on the space L1ðK; Þ. Finally we apply the results to polynomial hypergroups and obtain a rather complete solution for this class.
A noncommutative discrete hypergroup associated with qdisk polynomials
 J. Comp. Appl. Math
, 1996
"... Keywords and phrases: qdisk polynomials, linearization coefficients, DJShypergroup. ..."
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Keywords and phrases: qdisk polynomials, linearization coefficients, DJShypergroup.
Discrete hypergroups associated with compact quantum Gelfand pairs
 in Applications of Hypergroups and Related Measure Algebras
, 1995
"... Abstract. A discrete DJShypergroup is constructed in connection with the linearization formula for the product of two spherical elements for a quantum Gelfand pair of two compact quantum groups. A similar construction is discussed for the case of a generalized quantum Gelfand pair, where the role o ..."
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Abstract. A discrete DJShypergroup is constructed in connection with the linearization formula for the product of two spherical elements for a quantum Gelfand pair of two compact quantum groups. A similar construction is discussed for the case of a generalized quantum Gelfand pair, where the role of the quantum subgroup is taken over by a twosided coideal in the dual Hopf algebra. The paper starts with a review of compact quantum groups, with an approach in terms of socalled CQG algebras. The paper concludes with some examples of hypergroups thus obtained. 1.
Various amenability properties of the L1algebra of polynomial hypergroups and applications
"... We investigate amenability, weak amenability and αtamenability of the L1algebra of polynomial hypergroups, and derive from these properties some applications for the corresponding orthogonal polynomials. ..."
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We investigate amenability, weak amenability and αtamenability of the L1algebra of polynomial hypergroups, and derive from these properties some applications for the corresponding orthogonal polynomials.
On approximation methods by using orthogonal polynomial expansions
 in: Advanced Problems in Constructive Approximation, Birkhäuser
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Generalized hypergroups and orthogonal polynomials
 DEPARTMENT OF MATHEMATICS, M12, TECHNISCHE UNIVERSITÄT MÜNCHEN, BOLTZMANNSTR
"... The concept of semibounded generalized hypergroups (SBG hypergroups) is developed which are more special then generalized hypergroups introduced by Obata and Wildberger and which are more general then discrete hypergroups or even discrete signed hypergroups. The convolution of measures and function ..."
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The concept of semibounded generalized hypergroups (SBG hypergroups) is developed which are more special then generalized hypergroups introduced by Obata and Wildberger and which are more general then discrete hypergroups or even discrete signed hypergroups. The convolution of measures and functions is studied. In case of commutativity we define the dual objects and prove some basic theorems of Fourier analysis. Furthermore, we investigate the relationship between orthogonal polynomials and generalized hypergroups. We discuss the Jacobi polynomials as an example.
On αamenability of commutative hypergroups
"... We study the concept of αamenability of commutative hypergroups K. We establish several characterizations of αamenability by combining results of [1] and [2] and adding the GlicksbergReiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. ..."
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We study the concept of αamenability of commutative hypergroups K. We establish several characterizations of αamenability by combining results of [1] and [2] and adding the GlicksbergReiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed.
Orthogonal polynomials and Banach algebras
, 2001
"... Contents 1 Introduction 2 2 Introduction to orthogonal polynomials 3 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Differential equations . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 General orthogonal polynomials and recurrence relations . . . 7 2.4 Zeros of ..."
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Contents 1 Introduction 2 2 Introduction to orthogonal polynomials 3 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Differential equations . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 General orthogonal polynomials and recurrence relations . . . 7 2.4 Zeros of orthogonal polynomials . . . . . . . . . . . . . . . . . 10 3 Nonnegative linearization 11 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Renormalization . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 Discrete boundary value problem . . . . . . . . . . . . . . . . 18 3.5 Quadratic transformation . . . . . . . . . . . . . . . . . . . . 24 4 Commutative Banach algebras 26 4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Convolution associated with orthogonal polynomials . . . . . . 29 5
SPACES AND THE GENERALIZED CONCEPT OF NORMALITY
"... Abstract. The weighted Cesáro operator Ch in ℓ 2 (h)spaces is investigated in terms of several concepts of normality, where h denotes a positive discrete measure on N0. We classify exactly those h for which Ch is hyponormal. Two examples related to the Haar measures of orthogonal polynomials are di ..."
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Abstract. The weighted Cesáro operator Ch in ℓ 2 (h)spaces is investigated in terms of several concepts of normality, where h denotes a positive discrete measure on N0. We classify exactly those h for which Ch is hyponormal. Two examples related to the Haar measures of orthogonal polynomials are discussed. We show that the Cesáro operator is not always paranormal. Furthermore, we prove that the Cesáro operator is not quasinormal for any choice of h. 1. Introduction and
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