Fourier Transform of Unbounded Measures on Hypergroups

Massoud Amini

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On the Fourier Transformation of Positive, Positive Definite Measure on Commutative Hypergroups, and Dual Convolution Structures.

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Convolutions related to q-deformed commutativity

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Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution...

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The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.

Positive Characters on Commutative Hypergroups and Some applications.

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A limit theorem for the q-convolution

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The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...

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Vector-valued multipliers: convolution with operator-valued measures

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CONTENTS Preface.........................................................................................................5 1. Introduction...............................................................................................6 1.1. Measurability and vector measures.....................................................6 1.2. Convolution and vector measures.....................................................12 ...

Convolution in Colombeau's spaces of generalized functions. II: The convolution in $𝒢_{a}$ .

Nedeljkov, M., Pilipović, S. (1992)

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New Examples of Convolutions and Non-Commutative Central Limit Theorems

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A family of transformations on the set of all probability measures on the real line is introduced, which makes it possible to define new examples of convolutions. The associated central limit theorems are studied, and examples of the limit measures, related to the classical, free and boolean convolutions, are shown.