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The course is devoted to basic results from the theory of compact operators, theory of Sobolev spaces and applications of spectral theory. It contains the theory of compact symmetric operators and operational calculus of continuous linear operators in Hilbert and Banach spaces. Also some important results from the theory of Sobolev spaces are explained.
Last update: Knobloch František, PhDr., CSc. (10.02.2007)
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The course gives students a knowledge of the spectral theory of compact and special operators and of operator calculus. Last update: T_KNM (16.05.2008)
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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 Last update: T_KNM (16.05.2008)
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Lectures and tutorials in a lecture hall. Last update: T_KNM (16.05.2008)
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Examination according to the syllabus. Last update: T_KNM (16.05.2008)
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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. Last update: T_KNM (16.05.2008)
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Students are expected to have attended a basic course of functional analysis. Last update: T_KNM (16.05.2008)
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