 
|
|
|
|
|
|
|
|
|
MAM091 Functional Analysis 6.0 ECTS credits | |
|
TIMEPERIOD: Q IV LANGUAGE:English/Swedish EXAMINER L Maligranda Prof PREREQUISITES COURSE AIM This course is intended to familiarize the students with the basic concepts, principles and methods of functional analysis and its applications. CONTENTS 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 C[a,b], 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 TEACHING EXAMINATION The examination consists of a written exam at the end of the course. COURSE GRADE SCALE: ITEMS/CREDITS | |
| Written exam | 6.00ECTS |
|
COURSE LITERATURE Kreyszig E.: Introductory Functional Analysis with Applications. John Wiley 1978. Course information from the department: http://www.sm.luth.se/math/education/ |
Web Editor: Karin.Lindholm@dc.luth.se
| The University | Student | Research | Search | Contact us | In Swedish |
 LULEÅ UNIVERSITY OF TECHNOLOGY University Campus, Porsön, 971 87 Luleå. Tel. +46 (0) 920-91 000, fax +46 (0) 920-91 399 |