Extending wavelet filters: Infinite dimensions, the nonrational case, and indefinite inner product spaces

Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

6 Scopus citations

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.

Original languageEnglish
Title of host publicationExcursions in Harmonic Analysis
Subtitle of host publicationThe February Fourier Talks at the Norbert Wiener Center
PublisherBirkhauser Boston
Pages69-111
Number of pages43
Volume2
ISBN (Electronic)9780817683795
ISBN (Print)9780817683788
DOIs
StatePublished - 1 Jan 2013

Keywords

  • Cuntz relations
  • Pontryagin spaces
  • Schur analysis
  • Wavelet filters

Fingerprint

Dive into the research topics of 'Extending wavelet filters: Infinite dimensions, the nonrational case, and indefinite inner product spaces'. Together they form a unique fingerprint.

Cite this