| Description |
1 online resource (460 pages) |
| Series |
Applied and Numerical Harmonic Analysis |
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Applied and numerical harmonic analysis.
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| Contents |
Excursions in HarmonicAnalysis, Volume 2; ANHA Series Preface; Preface; Acknowledgments; Contents; Part V Measure Theory; Absolute Continuity and Singularity of Measures Without Measure Theory; References; Visible and Invisible Cantor Sets; 1 Introduction; 2 Terminology and Notation; 3 Visible Sets; 3.1 H-Visibility; 3.2 Generic Visibility; 4 Davies Sets in Polish Abelian Groups; References; Convolution Inequalities for Positive Borel Measures on Rd and Beurling Density; 1 Introduction; 2 Convolution of Positive Borel Measures; 3 Translation-Bounded Measures and Beurling Densities |
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4 Convolution Inequalities and Beurling Densities5 Vector-Valued Measures; References; Positive-Operator-Valued Measures: A General Setting for Frames; 1 Introduction; 2 Analysis and Synthesis; 3 Positive-Operator-Valued Measures; 4 Spectral Measures and the Naimark Theorem; 5 Analysis and Synthesis for General POVMs; 6 Isomorphism of POVMs; 7 Canonical Representations and POVMs; 8 Dual POVMs; 9 Radon-Nikodym Theorem for POVMs; 10 Conclusions; References; Part VI Filtering; Extending Wavelet Filters: Infinite Dimensions, the Nonrational Case, and Indefinite Inner Product Spaces |
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1 Introduction2 Some Background; 2.1 Cuntz Relations; 2.2 Wavelet Filters; 3 Pontryagin Spaces and Krein Spaces; 3.1 Krein Spaces; 3.2 Operators in Krein and Pontryagin Spaces; 3.3 Kernels; 4 Generalized Schur Functions; 4.1 Generalized Schur Functions; 4.2 State Spaces and Realizations; 4.3 Coisometric and Unitary Realizations; 4.4 Finite-Dimensional de Branges Spaces; 5 Cuntz Relations; 5.1 Cuntz Relations and the de Branges-Rovnyak Spaces; 5.2 Cuntz Relation: The General Case; 5.3 Cuntz Relations: Realizations in the Rational Case; 6 Decompositions |
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6.1 Generalized Down-Sampling and an Hermitian Form6.2 Orthogonal Decompositions in Krein Spaces; 6.3 Decompositions in Reproducing Kernel Spaces; 7 The Family CN; 7.1 The Family CN: Characterization; 7.2 A Connection with Periodic Systems; References; On the Group-Theoretic Structure of Lifted Filter Banks; 1 Introduction; 1.1 Perfect Reconstruction Filter Banks; 1.2 The Polyphase-with-Advance Representation; 1.3 Linear Phase Filter Banks; 2 Lifting Factorization of Linear Phase Filter Banks; 2.1 Lifting Factorizations; 2.2 Whole-Sample Symmetric Filter Banks |
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2.3 Half-Sample Symmetric Filter Banks3 Uniqueness of Linear Phase Lifting Factorizations; 3.1 Group Lifting Structures; 3.1.1 Lifting Matrix Groups; 3.1.2 Gain-Scaling Automorphisms; 3.1.3 Definition of Group Lifting Structures; 3.2 Unique Irreducible Group Lifting Factorizations; 3.2.1 An Abstract Uniqueness Theorem; 3.2.2 Application to WS and HS Group Lifting Structures; 4 Group-Theoretic Structure of Linear Phase Filter Banks; 4.1 Free Product Structure of Lifting Cascade Groups; 4.1.1 Lifting Cascade Groups Are Free Products of U and L |
| Summary |
The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts:Volume I· Sampling Theory· |
| Notes |
Print version record |
| Subject |
Harmonic analysis -- Congresses
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MATHEMATICS -- Infinity.
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Análisis armónico -- Congresos
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Harmonic analysis
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| Genre/Form |
proceedings (reports)
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Conference papers and proceedings
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Conference papers and proceedings.
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Actes de congrès.
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| Form |
Electronic book
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| Author |
Balan, Radu Victor, 1969-
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Benedetto, John.
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Czaja, Wojciech
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Okoudjou, Kasso A
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| ISBN |
9780817683795 |
|
0817683798 |
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081768378X |
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9780817683788 |
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