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Super-Wavelets Versus Poly-Bergman Spaces

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Abstract

We investigate a vector-valued version of the classical continuous wavelet transform. Special attention is given to the case when the analyzing vector consists of the first elements of the basis of admissible functions, namely the functions whose Fourier transform is a Laguerre function. In this case, the resulting spaces are, up to a multiplier isomorphism, poly-Bergman spaces. To demonstrate this fact, we introduce a new map and call it the polyanalytic Bergman transform. Our method of proof uses Vasilevski’s restriction principle for Bergman-type spaces. The construction is based on the idea of multiplexing of signals.

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Authors and Affiliations

  1. CMUC, Department of Mathematics of University of Coimbra, Portugal and NuHAG, Faculty of Mathematics, University of Vienna, Vienna, Austria

    Luis Daniel Abreu

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  1. Luis Daniel Abreu
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Correspondence to Luis Daniel Abreu.

Additional information

Partially supported by CMUC-FCT (Portugal) through European program COMPETE/FEDER and project PTDC/MAT/114394/2009, POCI 2010 and FSE and by Austrian Science Foundation (FWF) Project “ Frames and Harmonic Analysis”.

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Abreu, L.D. Super-Wavelets Versus Poly-Bergman Spaces. Integr. Equ. Oper. Theory 73, 177–193 (2012). https://doi.org/10.1007/s00020-012-1956-x

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  • DOI: https://doi.org/10.1007/s00020-012-1956-x

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