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Hyperbolic Wavelet Frames and Multiresolution in the Weighted Bergman Spaces

  • Margit PapEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

In this paper, we construct so-called hyperbolic wavelet frames in weighted Bergman spaces and a multiresolution analysis (MRA) generated by them. The construction is based on a new example of sampling set for the weighted Bergman space, which is related to the Blaschke group operation. The introduced MRA is an analog of the MRA generated by the affine wavelets in the space of the square integrable functions on the real line, and in fact is the discretization of the continuous voice transform generated by a representation of the Blaschke group over the weighted Bergman space. The projection to the resolution levels is an interpolation operator. This projection operator gives opportunity of practical realization of the hyperbolic wavelet representation of a function belonging to the weighted Bergman space, if we can measure the values of the function on a given set of points inside the unit disc. Convergence properties of the hyperbolic wavelet representation are studied.

Keywords

Voice transform Weighted Bergman spaces Frames Wavelets Multiresolution analysis 

2010 Mathematics Subject Classification:

43A32 42C40 33C47 43A65 

Notes

Acknowledgements

This research was supported by the grant EFOP-3.6.1.-16-2016-00004 Comprehensive Development for Implementing Smart Specialization Strategies at the University of Pécs.

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Authors and Affiliations

  1. 1.University of PécsPécsHungary

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