Course detail
Functional Analysis II
FSI-SU2Acad. year: 2010/2011
Revision of topics presented in the course Functional Analysis I. Functionals, dual spaces. Theory of linear operators. Compact sets and operators. Inversion of bounded linear operators. Spectral theory of compact operators.
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Planned learning activities and teaching methods
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Aims
Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
A.N.Kolmogorov, S.V.Fomin: Základy teorie funkcí a funkcionální analýzy, SNTL, Praha 1975. (CS)
L.Debnath, P.Mikusinski: Introduction to Hilbert spaces with Applications. 2-nd ed., Academic Press, London, 1999. (EN)
Recommended reading
A.Ženíšek: Funkcionální analýza II, skripta FSI VUT, PC-DIR, Brno 1999. (CS)
J. Kačur: Vybrané kapitoly z matematickej fyziky I, skripta MFF UK, Bratislava 1984. (CS)
L.A.Ljusternik, V.J.Sobolev: Elementy funkcionalnovo analiza, (CS)
Classification of course in study plans
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Lecture
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Syllabus
2. Projection, factorspace.
3. Orthogonal basis, abstract Fourier series.
4. Continuous linear functionals, Hahn-Banach theorem.
5. Weak convergence.
6. Linear operators, Banach-Steinhaus theorem.
7. Adjoint operator.
8. Compact sets and compact operators.
9. Inversion of linear operators in Banach and Hilbert spaces.
10. Spectral theory of linear compact operators.
11. Hilbert-Schmidt theorem.
12. Examples and applications.
13. Reserve.
Exercise
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