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Wavelets in mathematical physics: q-oscillators

Palle E T Jorgensen1 and Anna Paolucci2

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We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz algebra arising from this multiresolution analysis are contained as a special case in the Fock space construction.


PACS

02.30.Uu Integral transforms

02.30.Tb Operator theory

02.10.Yn Matrix theory

MSC

47L30 Abstract operator algebras on Hilbert spaces

47B37 Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

65T60 Wavelets

Subjects

Mathematical physics

Dates

Issue 23 (13 June 2003)

Received 11 December 2002, in final form 22 April 2003

Published 29 May 2003



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