Methods of Applied Fourier Analysis
Jayakumar Ramanathan
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Methods of Applied Fourier Analysis

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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...