FOURIER ANALYSIS

Introduction to Fourier Series; Plancherel theorem, basis approximation theorem, Dini's Condition etc. Introduction to Fourier transform; Plancherel theorem, 

Wiener Tauberian theorems, Interpolation of operators, Maximal functions, Lebesgue differentiation theorem, Poisson representation of harmonic functions, 

introduction to singular integral operators.

Books

• Dym, H. and Mckean, H.P., Fourier series and integrals, 1972.

• Stein, E.M., Singular integrals and differentiability properties of functions, 1970.

• Stein, E.M., and Weiss, G., Introduction to fourier analysis on Euclidean spaces, 1975.

• Sadosky, C., Interpolation of operators and singular integrals, 1979.