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Balian-Low phenomena, exponential bases and neural network approximation

  • The present cumulative thesis is based on 6 papers concerning 3 topics: Balian-Low theorems, exponential bases and neural network approximation. Various extensions of the Balian-Low theorem are proved for Gabor spaces spanning strict subsets of the space of square-integrable functions on the real line. Concerning exponential bases, we show that a partition of the unit interval into subintervals with rationally independent endpoints admits a so-called hierarchical Riesz spectral set. Finally, in terms of neural network approximation, quantitative rates for the approximation of complex valued functions with Sobolev (real) regularity via complex valued neural networks are obtained. Additionally, a network architecture is provided for approximating classifier functions with Barron boundaries without the curse of dimensionality.

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Metadaten
Author:Caragea, Andrei
URN:urn:nbn:de:bvb:824-opus4-9088
DOI:https://doi.org/10.17904/ku.opus-908
Subtitle (English):[cumulative dissertation]
Advisor:Prof. Dr. Pfander, Goetz, Prof. Dr. Walnut, David
Document Type:Doctoral thesis
Language of publication:English
Year of creation:2024
Date of first Publication:2024/05/27
Publishing Institution:Katholische Universität Eichstätt-Ingolstadt
Awarding Institution:Katholische Universität Eichstätt-Ingolstadt, Mathematisch-Geographische Fakultät
Date of final examination:2023/05/23
Release Date:2024/05/27
GND Keyword:Funktionalanalysis; Zeit-Frequenz-Analyse; Nichtharmonische Fourier-Reihe; Feedforward-Netz
Pagenumber:203, 14 Seiten : Diagramme
Faculty:Mathematisch-Geographische Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik
MSC-Classification:41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx)
42-XX FOURIER ANALYSIS
43-XX ABSTRACT HARMONIC ANALYSIS (For other analysis on topological and Lie groups, see 22Exx)
46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx)
License (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International
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