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AuthorRamanathan, Jayakumar. author
TitleMethods of Applied Fourier Analysis [electronic resource] / by Jayakumar Ramanathan
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1756-5
Descript XII, 329 p. online resource

CONTENT

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 Szegรถ-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 Bochnerโ{128}{153}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 An Approximation 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


Mathematics Fourier analysis Applied mathematics Engineering mathematics Computer mathematics Mathematical models Mathematics Fourier Analysis Mathematical Modeling and Industrial Mathematics Applications of Mathematics Computational Science and Engineering



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