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" New Trends in Applied Harmonic Analysis. "
Akram Aldroubi, Carlos Cabrelli, Stéphane Jaffard, Ursula Molter, editors.
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BL
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| Record Number
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862982
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| Title & Author
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New Trends in Applied Harmonic Analysis.\ Akram Aldroubi, Carlos Cabrelli, Stéphane Jaffard, Ursula Molter, editors.
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| Publication Statement
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Cham, Switzerland :: Birkhäuser,, [2019]
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| Series Statement
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Applied and Numerical Harmonic Analysis
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| Page. NO
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1 online resource (335 pages)
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| ISBN
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3030323536
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: 9783030323530
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9783030323523
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| Notes
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6 Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets
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| Bibliographies/Indexes
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Includes bibliographical references.
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| Contents
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Intro; ANHA Series Preface; Foreword; Preface; Acknowledgements; Contents; 1 CAZAC Sequences and Haagerup's Characterization of Cyclic N-roots; 1.1 Introduction; 1.1.1 Background and Goal; 1.1.2 Gaussian and Non-Gaussian CAZAC Sequences; 1.1.3 Haagerup's Theorem; 1.1.4 Outline; 1.2 Characterizations and Properties of CAZAC Sequences; 1.2.1 Characterizations of CAZAC Sequences; 1.2.2 Equivalence Classes of CAZAC Sequences; 1.2.3 Cyclic p-roots; 1.2.4 CAZAC Sequences of Non-square-free Length; 1.2.5 Dephased Hadamard Matrices; 1.3 Roots of Unity CAZAC Sequences of Prime Length
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1.3.1 Introduction1.3.2 Constructing CAZAC Sequences of Length 3 Using Cyclic 3-roots; 1.3.3 Constructing CAZAC Sequences of Length 3 Using Hadamard Matrices; 1.3.4 5-Operation Equivalence Relations; 1.3.5 5-Operation Equivalence for Lengths 3 and 5; 1.4 Non-roots of Unity CAZAC Sequences of Prime Length; 1.4.1 Björck sequences of prime length; 1.4.2 Circulant Hadamard Matrices not Equivalent to mathcalD7; 1.5 Haagerup's Theorem; 1.5.1 Introduction; 1.5.2 Algebraic Manipulation; 1.5.3 The Uncertainty Principle for mathbbZ/pmathbbZ; 1.6 Appendix-Real Hadamard Matrices; References
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2 Hardy Spaces with Variable Exponents2.1 Introduction; 2.2 Lebesgue Spaces with Variable Exponents; 2.3 Hardy Spaces with Variable Exponents; 2.4 Hardy Spaces with Variable Exponents Associated with Operators; 2.5 Local Hardy Spaces with Variable Exponents; References; 3 Regularity of Maximal Operators: Recent Progress and Some Open Problems; 3.1 Introduction; 3.2 Kinnunen's Seminal Work; 3.3 The Endpoint Sobolev Space; 3.3.1 One-Dimensional Results; 3.3.2 Multidimensional Results; 3.4 Maximal Operators of Convolution Type; 3.5 Fractional Maximal Operators; 3.6 Discrete Analogues
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3.6.1 One-Dimensional Results3.6.2 Multidimensional Results; 3.7 Continuity; 3.7.1 Endpoint Study; 3.7.2 Fractional Setting; 3.7.3 Discrete Setting; 3.7.4 Summary; References; 4 Gabor Frames: Characterizations and Coarse Structure; 4.1 Introduction; 4.2 The Objects of Gabor Analysis; 4.3 Commutation Rules and the Poisson Summation Formula in Gabor Analysis; 4.3.1 Poisson Summation Formula; 4.3.2 Commutation Rules; 4.4 Duality Theory; 4.5 The Coarse Structure of Gabor Frames; 4.5.1 Density Theorem; 4.5.2 Existence of Gabor Frames for Sufficiently Dense Lattices; 4.5.3 Balian-Low Theorem
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4.5.4 The Coarse Structure of Gabor Frames and Gabor Riesz Sequences4.6 The Criterion of Janssen, Ron, and Shen for Rectangular Lattices; 4.7 Zak Transform Criteria for Rational Lattices-The Criteria of Zeevi and Zibulski; 4.8 Further Characterizations; 4.8.1 The Wiener Amalgam Space and Irrational Lattices; 4.8.2 Janssen's Criterion Without Inequalities; 4.8.3 Gabor Frames Without Inequalities; References; 5 On the Approximate Unit Distance Problem; 5.1 Introduction; 5.1.1 Sharpness of Results; 5.2 Proof of Theorem 5.1.2; 5.2.1 Proof of Lemma 5.1.6; References
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| Subject
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Harmonic analysis.
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| Subject
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Harmonic analysis.
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| Dewey Classification
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515/.2433
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| LC Classification
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QA1-939
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QA403.N49 2019
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| Added Entry
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Aldroubi, Akram
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Cabrelli, Carlos A,1949-
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Jaffard, Stéphane,1962-
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Molter, Ursula M.,1957-
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| Parallel Title
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Harmonic Analysis, Geometric Measure Theory, and Applications
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