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Last update: PhDr. František Knobloch, CSc. (10.02.2007)
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Last update: T_KNM (16.05.2008)
The course gives students a knowledge of the spectral theory of compact and special operators and of operator calculus. |
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Last update: T_KNM (16.05.2008)
Taylor A.E.: Úvod do funkcionální analýzy, l973 Blank J., Exner P.,Havlíček M.: Lineární operátory v kvantové fyzice, l990 Kato T.: Perturbation theory for linear operators, 1966, (v ruštině 1972) Najzar K. : Funkcionální analýza, skripta, l988 Fučík S., John O., Kufner A.: Prostory funkcí, 1974, skripta Kufner, A. John O., Fučík S.: Function spaces, 1977 |
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Last update: T_KNM (16.05.2008)
Lectures and tutorials in a lecture hall. |
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Last update: T_KNM (16.05.2008)
Examination according to the syllabus. |
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Last update: T_KNM (16.05.2008)
Spectral analysis of symmetric linear operators in Hilbert spaces. Self-adjoint and normal operators. The theory of compact symmetric operators and Hilbert-Schmidt theory. The spectral theorem for compact and self-adjoint operators. The operational calculus founded on contour integrals. Isolated point of spectrum and Laurent expansion of the resolvent of a linear continuous operator in Banach spaces. Operators of finite rank, nuclear and Hilbert-Shmidt operators, Fredholm's operators. Distributions and Sobolev spaces. Introduction to the theory of perturbations. |
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Last update: T_KNM (16.05.2008)
Students are expected to have attended a basic course of functional analysis. |