Frame structure derived from a non-Blaschke sequence on the unit disc

In this article, we examine Rational Blaschke functions to create the Multiresolution analysis on the Hardy space H 2 ( 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 a...

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Bibliographic Details
Published in:The Journal of Analysis 2024-08, Vol.32 (4), p.2281-2297
Main Authors: Sreedharan, Anusree, Asharaf, Noufal
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Fourier Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Measure and Integration
Original Research Paper
Special Functions
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Summary:In this article, we examine Rational Blaschke functions to create the Multiresolution analysis on the Hardy space H 2 ( 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.
ISSN:0971-3611
2367-2501
DOI:10.1007/s41478-023-00705-0