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Displaying similar documents to “Boehmians on manifolds.”

A limit theorem for the q-convolution

Anna Kula (2011)

Banach Center Publications

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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...

On the incomplete gamma function and the neutrix convolution

Brian Fisher, Biljana Jolevska-Tuneska, Arpad Takači (2003)

Mathematica Bohemica

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The incomplete Gamma function γ ( α , x ) and its associated functions γ ( α , x + ) and γ ( α , x - ) are defined as locally summable functions on the real line and some convolutions and neutrix convolutions of these functions and the functions x r and x - r are then found.

Convolutions related to q-deformed commutativity

Anna Kula (2010)

Banach Center Publications

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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...