Mathematics BSc
Course description
2013.
Course description
2013.
Functional Analysis
Hours lect+pc |
Credits lect+pc |
Assessment | Specialization | Course code lect/pc |
Semester | Status |
---|---|---|---|---|---|---|
2 + 2 | 2 + 3 | exam + term grade |
pure math. | mm1c1fa5m mm1c2fa5m |
5 | compulsory |
Course coordinator
Strong | Weak | Prerequisites | |
---|---|---|---|
Practice class | |||
Strong:
| |||
Lecture | |||
Weak:
practice class
| |||
Weak:
Analysis3L-p
(mm1c1an3m)
|
Prerequisites
Analysis 3, notion of Lebesgue integral, linear algebra.
Literature
- F. Riesz, B. Szőkefalvi: Functional Analysis. Dover, 1990.
Syllabus
- Hilbert spaces: inner product, Cauchy-Bunyakovsky-Schwarz inequality, ℓ2, L2 spaces, distance from closed subspace, orthonormal basis, Fourier series, Bessel's inequality, Parseval's identity, continuous linear functionals on Hilbert spaces, Riesz's theorem.
- Continuous linear operators in Hilbert spaces: norm, numerical radius, adjoint, spectrum, selfadjoint, normal, unitary operators, orthogonal projections, compact operators in Hilbert spaces, Hilbert-Schmidt theorem.
- Banach spaces: distance from subspace, Riesz's lemma, Baire category theorem, continuous linear functionals, Hahn-Banach theorem, Mazur-Orlicz theorem, continuous linear operators, adjoint, spectrum, Neumann series, Banach-Steinhaus theorem, uniform boundedness principle, Banach open mapping theorem, closed graph theorem, compact operators in Banach spaces, Riesz-Fredholm theory, Schauder's theorem, Lomonosov's theorem.