Credits: 3 (3-0-0)
Description
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.
Prerequisite Tree
flowchart TD
MTL743-1016[MTL743]
MTL743-1016 --- Or1017[Any one of]:::empty
Or1017 -.-> MTL122-1018[MTL122]
MTL122-1018 --> MTL100-1018[MTL100]
Or1017 -.-> MTL503-1019[MTL503]
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