SubjectsSubjects(version: 953)
Course, academic year 2023/2024
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Functional Analysis - NMNV401
Title: Funkcionální analýza
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. RNDr. Jiří Felcman, CSc.
Class: M Mgr. NVM
M Mgr. NVM > Povinné
Classification: Mathematics > Functional Analysis
Incompatibility : NRFA017
Interchangeability : NRFA017
Is interchangeable with: NRFA017
Annotation -
Necessary and sufficient conditions for the solvability of abstract variational problem in Banach spaces. Saddle-point problems. Spectral analysis of symmetric linear operators in Hilbert space. Self-adjoint and normal operators. Spectral theorem for compact and self-adjoint operators. Operator calculus. Spectral analysis of continuous linear operator in Banach space. Special operators. The subject is compulsory for the branch Numerical and computational mathematics.
Last update: T_KNM (14.04.2015)
Course completion requirements -

Credit for the exercise is granted for continuous activity at the exercise and continuous homework throughout the semester.

Last update: Felcman Jiří, doc. RNDr., CSc. (13.10.2017)
Literature -

A.E. Taylor: Úvod do funkcionální analýzy, Academia, l973

K. Yosida: Functional analysis, Springer-Verlag, 1980

K. Najzar: Funkcionální analýza, skripta MFF UK, 1988

A. Kufner, O. John, S. Fučík: Function spaces, Academia, 1977

Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
Requirements to the exam -

The exam is written and oral. The examination requirements are given by the topics in the syllabus, in the extent to which they they were taught in course.

Last update: Felcman Jiří, doc. RNDr., CSc. (13.10.2017)
Syllabus -

Necessary and sufficient condition for solution of abstract saddle-point problem in Banach spaces. Saddle-point problems. The spectral theorem for compact and self-adjoint operators. Self-adjoint and normal operators. Operator calculus. Spectral analysis of continuous linear operator in Banach spaces. Special operators.

Last update: T_KNM (15.09.2013)
Entry requirements -

Basic knowledge of the functional analysis from the bachelor study

Last update: Felcman Jiří, doc. RNDr., CSc. (31.05.2018)
 
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