Convolutions related to q-deformed commutativity

• Autorzy: Anna Kula
• Języki publikacji: EN

Abstrakty

EN

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 of measures based on the so-called (p,q)-commutativity, a generalization of ab = qba. We investigate and compare properties of both convolutions (associativity, commutativity and positivity) and corresponding Fourier transforms.

Kategorie tematyczne

• 46L53: Noncommutative probability and statistics
• 42A85: Convolution, factorization
• 05A30: q -calculus and related topics
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 89
• Numer: 1
• Strony: 189-200

Daty

wydano

2010

Twórcy

autor

Anna Kula

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 4, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/bc89-0-11