Math 627, Introduction to Fourier Analysis

Syllabus:[pdf] Schedule of material covered 1st week, Sept. 810 Origin of Fourier series: wave equation 2nd week, Sept. 1318 Orthogonal sequences, trig. Fourier series and its properties 3rd week, Sept. 2025 Fourier series, convolutions, Wiener's algebra 4th week, Sept. 27 Oct. 1 Convergence of Fourier series 5th week, Oct. 48 Convergence of Fourier series 6th week, Oct. 1115 Convergence of Fourier series, Poisson kernel, Abel's summation 7th week, Oct. 1822 Polynomial inequalities (Bernstein, Nikolskii) and applications 8th week, Oct. 2529 Random and lacunary polynomials, RudinShapiro polynomials 9th week, Nov. 15 Lacunary polynomials, Finite Fourier Analysis and FFT 10th week, Nov. 812 Fourier integrals 11th week, Nov. 1519 Fourier integral and applications 12th week, Nov. 2224 Fourier integral and applications, heat equation 13th week, Nov. 29 Dec. 3 Fourier integrals in higher dimension 14th week, Dec. 6 Dec. 10 Some applications 15th week, Dec. 13 Dec. 15 Some
applications 
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