Book chapter
Extending Wavelet Filters: Infinite Dimensions, the Nonrational Case, and Indefinite Inner Product Spaces
Excursions in Harmonic Analysis, Volume 2, pp.69-111
Applied and Numerical Harmonic Analysis, Birkhäuser Boston
11/23/2012
DOI: 10.1007/978-0-8176-8379-5_5
Abstract
In this chapter we are discussing various aspects of wavelet filters. While there are earlier studies of these filters as matrix-valued functions in wavelets, in signal processing, and in systems, we here expand the framework. Motivated by applications and by bringing to bear tools from reproducing kernel theory, we point out the role of non-positive definite Hermitian inner products (negative squares), for example, Krein spaces, in the study of stability questions. We focus on the nonrational case and establish new connections with the theory of generalized Schur functions and their associated reproducing kernel Pontryagin spaces and the Cuntz relations.
Details
- Title: Subtitle
- Extending Wavelet Filters: Infinite Dimensions, the Nonrational Case, and Indefinite Inner Product Spaces
- Creators
- Daniel Alpay - Ben-Gurion University of the NegevPalle Jorgensen - Department of Mathematics, The University of Iowa City, Iowa City, USAIzchak Lewkowicz - Ben-Gurion University of the Negev
- Resource Type
- Book chapter
- Publication Details
- Excursions in Harmonic Analysis, Volume 2, pp.69-111
- Series
- Applied and Numerical Harmonic Analysis
- DOI
- 10.1007/978-0-8176-8379-5_5
- eISSN
- 2296-5017
- ISSN
- 2296-5009
- Publisher
- Birkhäuser Boston; Boston
- Language
- English
- Date published
- 11/23/2012
- Academic Unit
- Mathematics
- Record Identifier
- 9984240762302771
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