Extending Wavelet Filters: Infinite Dimensions, the Nonrational Case, and Indefinite Inner Product Spaces

DOI10.1007/978-0-8176-8379-5_5zbMath1311.65176arXiv1106.2303OpenAlexW1616172839MaRDI QIDQ5244605

Izchak Lewkowicz, Palle E. T. Jorgensen, Daniel Alpay

Publication date: 27 March 2015

Published in: Excursions in Harmonic Analysis, Volume 2 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2303

zbMATH Keywords

stabilityKrein spacesignal processingwavelet filtersPontryagin spacesSchur analysisCuntz relations

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Numerical methods for wavelets (65T60) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20)

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A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions ⋮ A Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes ⋮ Reflection positivity via Krein space analysis ⋮ Reproducing kernels: harmonic analysis and some of their applications ⋮ Representation theory and multilevel filters ⋮ Herglotz functions: the Fueter variables case ⋮ 𝑊-Markov measures, transfer operators, wavelets and multiresolutions ⋮ Realizations of infinite products, Ruelle operators and wavelet filters

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