2019/2020
Научно-исследовательский семинар "Конструктивные методы функционального анализа"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
3, 4 модуль
Преподаватели:
Погребков Андрей Константинович
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
This is a version of the standard course «Functional Analysis– 2» oriented to various applications of the theory, especially in mathematical physics. We consider distributions, regularization, unbounded operators in the Hilbert space, the Fourier transform, etc.
Learning Objectives
- Students will gain an understanding of the main ideas of the modern mathematical physics
Expected Learning Outcomes
- Students will be able to use methods of theory of distributions
- Students will be able to perform Fourier transform
- Students will be able to use methods of spectral theory of unbounded operators and some others in their individual work
Course Contents
- Different spaces of distributions, local properties, regularization, convergence of distributions
- Sokhotski–Plemelj formulas, limiting values of holomorphic functions
- Fourier transform, fundamental solutions of PDE’s
- Unbounded operators in the Hilbert space, domains and graphs, conjugate operators, spectrum
- Topologies on the space of unbounded operators
- Symmetric and self-adjoint operators, the spectral theorem, the Stone theorem
- Tensor products
Assessment Elements
- cumulative gradecumulative grade is proportional to the number of solved problems (so that 10 corresponds to 75% of all problems), rounded to the nearest integer (half-integers are rounded upwards). Active participants will get bonuses.
- Final exam
Bibliography
Recommended Core Bibliography
- Reed, M. (1972). Methods of Modern Mathematical Physics : Functional Analysis. Oxford: Academic Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=567963
Recommended Additional Bibliography
- Aydın Aytuna, Reinhold Meise, Tosun Terzioğlu, & Dietmar Vogt. (2011). Functional Analysis and Complex Analysis. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=974875