Methods of Applied Fourier Analysis
Language: English
Published by Springer Nature B.V. Aug 1998, 1998
Series: Book 3 of 88 - Applied and Numerical Harmonic Analysis
- Hardcover
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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Neuware - 1 Periodic Functions.- 1.1 The Characters.- 1.2 Some Tools of the Trade.- 1.3 Fourier Series: Lp Theory.- 1.4 Fourier Series: L2 Theory.- 1.5 Fourier Analysis of Measures.- 1.6 Smoothness and Decay of Fourier Series.- 1.7 Translation Invariant Operators.- 1.8 Problems.- 2 Hardy Spaces.- 2.1 Hardy Spaces and Invariant Subspaces.- 2.2 Boundary Values of Harmonic Functions.- 2.3 Hardy Spaces and Analytic Functions.- 2.4 The Structure of Inner Functions.- 2.5 The H1 Case.- 2.6 The Szegö-Kolmogorov Theorem.- 2.7 Problems.- 3 Prediction Theory.- 3.1 Introduction to Stationary Random Processes.- 3.2 Examples of Stationary Processes.- 3.3 The Reproducing Kernel.- 3.4 Spectral Estimation and Prediction.- 3.5 Problems.- 4 Discrete Systems and Control Theory.- 4.1 Introduction to System Theory.- 4.2 Translation Invariant Operators.- 4.3 H Control Theory.- 4.4 The Nehari Problem.- 4.5 Commutant Lifting and Interpolation.- 4.6 Proof of the Commutant Lifting Theorem.- 4.7 Problems.- 5 Harmonic Analysis in Euclidean Space.- 5.1 Function Spaces on Rn.- 5.2 The Fourier Transform on L1.- 5.3 Convolution and Approximation.- 5.4 The Fourier Transform: L2 Theory.- 5.5 Fourier Transform of Measures.- 5.6 Bochner's Theorem.- 5.7 Problems.- 6 Distributions.- 6.1 General Distributions.- 6.2 Two Theorems on Distributions.- 6.3 Schwartz Space.- 6.4 Tempered Distributions.- 6.5 Sobolev Spaces.- 6.6 Problems.- 7 Functions with Restricted Transforms.- 7.1 General Definitions and the Sampling Formula.- 7.2 The Paley-Wiener Theorem.- 7.3 Sampling Band-Limited Functions.- 7.4 Band-Limited Functions and Information.- 7.5 Problems.- 8 Phase Space.- 8.1 The Uncertainty Principle.- 8.2 The Ambiguity Function.- 8.3 Phase Space and Orthonormal Bases.- 8.4 The Zak Transform and the Wilson Basis.- 8.5 AnApproximation Theorem.- 8.6 Problems.- 9 Wavelet Analysis.- 9.1 Multiresolution Approximations.- 9.2 Wavelet Bases.- 9.3 Examples.- 9.4 Compactly Supported Wavelets.- 9.5 Compactly Supported Wavelets II.- 9.6 Problems.- A The Discrete Fourier Transform.- B The Hermite Functions.…
Seller Inventory # 9780817639631
- Title
- Methods of Applied Fourier Analysis
- Author
- Jayakumar Ramanathan
- Publisher
- Springer Nature B.V. Aug 1998
- Publication year
- 1998
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 0817639632
- ISBN 13
- 9780817639631
- Item weight
- 682 grams
- Dimensions
- 241x160x24 mm
- Series
- Book 3 of 88: Applied and Numerical Harmonic Analysis
"Synopsis" may belong to another edition of this title.
Review
"The author has written a very careful, complete and readable introduction.... The treatment is mathematically sophisticated and precise.... This distinguishes the text and and makes it a very valuable reference for professionals interested in all relevant applications of Fourier analysis. This book would also be appropriate as a text for a graduate course in mathematics of advanced engineering."
―Mathematical Reviews
"About the title" may belong to another edition of this title.
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