Details of MA4205 (Spring 2020)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4205 | Fourier Analysis | Saugata Bandyopadhyay |
| Syllabus |
|---|
| Convolution: Convolution, elementary properties of convolutions.
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. Hardy-Littlewood Maximal Function: Approximations of the identity, weak-type in-equality, Marcinkiewicz interpolation theorem, Hardy-Littlewood maximal function and its properties, dyadic maximal function, Calderon-Zygmund theorem, Riesz-Thorin interpolation theorem. 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. |
| Prerequisite |
|---|
| Analysis IV (MA3204), Functional Analysis (MA4102) |
| References |
|---|
| 1. Duoandikoetxea, J., Fourier Analysis, American Mathematical Society.
2. Grafakos, L., Classical Fourier Analysis, Springer-Verlag. 3. Katznelson, Y., An Introduction to Harmonic Analysis, Cambridge University Press. 4. Krner, T.W., Fourier Analysis, Cambridge University Press. 5. Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press. 6. Stein, E.M. and Sakarachi, R., Fourier Analysis: An Introduction, Princeton Univer-sity Press. 7. Stein, E.M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course 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 | Elective |
| 7 | RS | 1 | Not Allowed |
| 8 | RS | 2 | Not Allowed |