|
HU Credits:
4
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Prof Alexander Sodin
Coordinator Office Hours:
Sundays 14:20-15:20 or by appointment
Teaching Staff:
Prof Alexander Sodin
Course/Module description:
The course will provide an introduction to harmonic analysis on the three simplest groups: circle, the integers, and the real numbers. We shall develop the general theory explaining how and in which sense can a function be approximated by linear combinations of "harmonics", and also provide applications in various parts of mathematics (analysis, partial differential equations, probability theory and number theory).
Course/Module aims:
Learning outcomes - On successful completion of this module, students should be able to:
apply the theory and methods of harmonic analysis.
Attendance requirements(%):
Teaching arrangement and method of instruction:
Three hours of lectures, and an hour devoted to the discussion of problems from the homework assignments.
Course/Module Content:
Fourier series:
– convergence and divergence in various senses
– Cesaro summation
– Wiener algebra and Wiener lemma
– Fourier series of measures
– Fourier series and complex analysis.
Applications:
– diagonalisation of operators commuting with shifts
– random walk on the lattice
– heat equation
– polynomial approximation
– the spectral theorem for unitary operators
– equidistribution modulo one
Fourier transformation:
– construction
– Poisson formula and applications
– additional topics
Required Reading:
-
Additional Reading Material:
Y. Katznelson, "Introduction to harmonic analysis"
H. Dym and H. McKean, "Fourier Series and Integrals"
H. Montgomery, "Early Fourier Analysis"
Grading Scheme :
Written / Oral / Practical Exam 70 %
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 30 %
Additional information:
|
