Details of MA4201 (Spring 2017)

Level: 4 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA4201 Fourier Analysis Rajib Dutta


  • Convolution: Convolution, elementary properties of convolutions.

  • The Hardy-Littlewood Maximal Function : Approximations of the identity, weak-type inequality, Marcinkiewicz Interpolation Theorem, Hardy-Littlewood maximal function and its properties, dyadic maximal function, Calderon-Zygmund theorem. Riesz-Thorin Interpolation Theorem.

  • Fourier Series: Fourier coefficients and series, summability in norm, summability at a point, Weiner Algebra, pointwise convergence of Fourier series, convergence of Fourier series in norm.

  • The Hilbert Transform: Conjugate Poisson kernel, principal value distribution, Riesz and Kolmogorov theorems, multipliers.

  • Fourier Transform: Fourier transform of $L^1$ functions, Schwartz class, Fourier transform for $ L^2$ functions, Plancherel theorem.

  • Fourier integrals: Summability in norm, pointwise summability and convergence in norm.


  1. J. Duoandikoetxea, Fourier Analysis, Graduate Studies in Mathematics, American Mathematical Society, 2001.

  2. L. Grafakos, Classical Fourier Analysis (2nd Edition), Springer-Verlag, 2008.

  3. Y. Katznelson, An Introduction to Harmonic Analysis (3rd Edition), Cambridge University Press, 2004.

  4. T. W. Krner, Fourier Analysis, Cambridge University Press, 1989.

  5. E. M. Stein and R. Sakarachi, Fourier Analysis: An Introduction, Princeton University Press, 2003.

    6. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton
    University Press, 1971.

    7. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton
    University Press, 1971.

University Press, 1971.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 2 Not Allowed
2 IP 4 Core
3 IP 6 Not Allowed
4 MR 2 Not Allowed
5 MR 4 Not Allowed
6 MS 8 Core
7 RS 1 Elective
8 RS 2 Not Allowed