Abstract
In this article, we examine Rational Blaschke functions to create the Multiresolution analysis on the Hardy space \(H_{2} (\mathbb {T})\). We discuss a decomposition using a non-Blashke sequence, which is analogous to the Whitney cube decomposition of the unit disc. Our primary goal is to successfully recreate an analytic function from samples at the non-Blaschke sequence. We explore the Banach frame structure that was produced from the non-Blaschke sequences, look at the frame structure of the reproducing kernel that corresponds to it, and derive a series representation of any operator in the space in terms of the sampling sequence.
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Acknowledgements
The authors acknowledge Dr. Margit Pap, Associate Professor, Department of Mathematics, University of Pecs for fruitful discussions in this research direction. Anusree Sreedharan wishes to thank Cochin University of Science and Technology for the PhD fellowship.
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Sreedharan, A., Asharaf, N. Frame structure derived from a non-Blaschke sequence on the unit disc. J Anal (2024). https://doi.org/10.1007/s41478-023-00705-0
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DOI: https://doi.org/10.1007/s41478-023-00705-0