MTL743

MTL743
Fourier Analysis
Credits	3
Structure	3-0-0
Pre-requisites	MTL122/MTL503
Overlaps

MTL743 : Fourier Analysis

Fourier Series - Definition, uniqueness, convolution, summability, convergence of Fourier series, Fourier series for square integrable functions, Plancheral theorem, Riesz-Fischer theorem, Gibb's phenomenon, divergence of Fourier series Applications of Fourier series – Isoperimetric inequality, Weierstrass approximation theorem, Weyl's equidistribution theorem, heat equation on the circle. Fourier transform – Schwartz space on R, Fourier transform on the Schwartz space, Fourier transform of integrable and square-integrable functions, Poisson summation formula. Tempered distributions – Topology on the Schwartz space, tempered distributions and its properties, Fourier transform of tempered distributions. Applications – Uncertainty principle, Paley-Wiener theorem, Wiener's theorem, Shannon sampling theorem, multiplier theorem for integrable functions.