| Area of Mathematics: | Analysis (EA) | ||
| Semester: | 8ο | ||
| Course ID: | 82101 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 4 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: |
Description
- Lebesgue measure and integral: The L1(A) space. Convergence calculations and theorems. Measure and integral on Rd. Fubini Theorem. The Lp(A)
- Trigonometric polynomials.
- Fourier coefficients of an integrable function and Fourier series. Fourier Series examples. Absolutely converging trigonometric series. Fourier factor size and function smoothness.
- Pointwise convergence of partial sums of the Fourier series. Principle of locality. Conditions that guarantee convergence of points.
- Summability of Fourier series. Uniqueness theorem. Linear and Circular Convolution. Dirichlet kernel. Cesáro means of the Fourier series and Fejér’s theorem. Weierstrass Theorem.
- L2 Theory
- Applications: The isoperimetric inequality. Weyl’s equidistribution theorem.
Bibliography
- Fourier Analysis : An Introduction , E.Stein , R.Shakarchi , Princeton Lectures in Analysis.
- Fourier Analysis and its Applications , G.Folland , Brooks/Cole Publishing 1992.
