Details of MA4201 (Spring 2013)
| Level: 4 | Type: Theory | Credits: 3.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4201 | Distribution Theory and Fourier Analysis | Saugata Bandyopadhyay |
| Syllabus |
|---|
| 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 L1 functions, Schwartz class, Fourier transform for L2 functions, Plancherel theorem. Fourier integrals: Summability in norm, pointwise summability and convergence in norm. |
| References |
|---|
| 1. Duoandikoetxea, J., Fourier Analysis, Graduate Studies in Mathematics, American Mathematical Society, 2001.
2. Grafakos, L., Classical Fourier Analysis (2nd Edition), Springer-Verlag, 2008. 3. Katznelson, Y., An Introduction to Harmonic Analysis (3rd Edition), Cambridge University Press, 2004. 4.Krner, T. W., Fourier Analysis, Cambridge University Press, 1989. 5. Stein, E. M. and Sakarachi, R., Fourier Analysis: An Introduction, Princeton University Press, 2003. 6. Stein, E. M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971. 7. Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1971. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Elective |
| 3 | MS | 8 | Core |
| 4 | RS | 1 | Elective |