Fourier Transform of Unbounded Measures on Hypergroups

Massoud Amini

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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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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 $𝒢_{a}$ .

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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.