Svenska Studiehandboken kurser

Matematik

MAM091 Funktionsanalys 4.0 Poäng

Program/Tidsperiod

F4, D4 / Lp IV

SPRÅK:

EXAMINATOR
L Maligranda Univ lekt

FASTSTÄLLD
Kursplanen är fastställd av Institutionen för matematik 1997-02-17 att gälla från H97.

FÖRKUNSKAPSKRAV

MÅL
This course is intended to familiarize the students with the basic concepts, principles and methods of functional analysis and its applications.

INNEHÅLL
Metric spaces, examples, open and closed sets, convergence, completeness; Normed and Banach spaces, examples, properties, finite dimensional spaces, compactness; Bounded linear operators and functionals, dual space; Inner product and Hilbert spaces, examples, properties, orthogonal projection, orthonormal sequences, Fourier series in Hilbert spaces, orthonormal polynomials, linear functionals on Hilbert space; The Hahn-Banach theorem, functionals on CÄa,bÅ, adjoint operators, reflexive spaces; Uniform boundedness theorem and some applications, strong and weak convergence, numerical integration; Open mapping theorem, closed graph theorem; Banach fixed point theorem, applications to linear, differential and integral equations; Approximation in normed spaces, uniquess and strict convexity, uniform approximation; Compact operators

UNDERVISNING

EXAMINATION
The examination consists of a written exam at the end of the course.
KURSENS BETYGSKALA: 3, 4, 5

MOMENT/PROV


Tentamen                                                    	  4.0	Poäng

LITTERATUR
Kreyszig E.: Introductory Functional Analysis with Applications, John Wiley 1978.

ÖVRIGT
The course will not be given 1997/98.

Last modified: 97-06-05by Jan Lindberg
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