Characterization of Convolution Operators on Spaces of C-Functions Admitting a Continuous Linear Right Inverse.
Dietmar Vogt, Reinhold Meise (1987/88)
Mathematische Annalen
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Displaying similar documents to “A positivity result and normalization of positive convolution structures.”
Characterization of Convolution Operators on Spaces of C-Functions Admitting a Continuous Linear Right Inverse.
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The paper is, for the most part, devoted to a survey of the analytical properties of generalized convolution algebras and their realizations. This issue appears to be the state of the art until now because intensive research on the generalized convolution and the related models still persists.
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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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