Mathematics BSc
Course description
2013.
Course description
2013.
Fourier integral
Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
---|---|---|---|---|---|---|
2 + 2 | 2 + 3 | exam + term grade |
pure math. | mm1c1fi6m mm1c2fi6m |
6 | recommended |
Course coordinator
Strong | Weak | Prerequisites | |
---|---|---|---|
Practice class | |||
Strong:
Analysis4L-p
(mm1c1an4m)
| |||
Strong:
Complex analysisP-p
(mm1c2kf5m)
| |||
Lecture | |||
Weak:
Practice class
|
Syllabus
- L1 theory. The Fourier integral of L1 functions. The Fourier integral of a convolution. The inverse formula.
- The Wiener approximation theorem. Application for Wiener's Tauber-type theorem.
- The Fourier integral of a complex measure. The Fourier integral of a measure with bounded variation. Inversion formula. Wiener's Parseval-type formula. Characterization of continuous measures.
- L2 theory. The Parseval formula.
- Convolution in Lp spaces. The Fourier transform of the derivative. The Young-Hausdorff inequality. The Riesz-Thorin theorem. The Marczinkiewicz interpolation theorem.
- The Fejér kernel. The estimation of the discrepancy due to Erdős and Turán. The estimation of the discrepancy due to Beck.
- The Selberg sieve. The Poisson formula. Application in number theory.
- The complex Fourier integral. The Paley-Wiener theorem.