SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Functional Analysis - NMNV401
Title in English: Funkcionální analýza
Guaranteed by: Department of Numerical Mathematics (32-KNM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2019
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
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
Annotation -
Last update: T_KNM (14.04.2015)
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.
Course completion requirements -
Last update: doc. RNDr. Jiří Felcman, CSc. (13.10.2017)

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

Literature
Last update: T_KNM (15.09.2013)

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

Requirements to the exam -
Last update: doc. RNDr. Jiří Felcman, CSc. (13.10.2017)

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.

Syllabus -
Last update: T_KNM (15.09.2013)

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.

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

Basic knowledge of the functional analysis from the bachelor study

 
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