406-3461-AAL Functional Analysis I
| Semester | Herbstsemester 2018 |
| Dozierende | M. Einsiedler |
| Periodizität | jedes Semester wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
| Kommentar | Belegung ist NUR erlaubt für MSc Studierende, die diese Lerneinheit als Auflagenfach verfügt haben. Alle andere Studierenden (u.a. auch Mobilitätsstudierende, Doktorierende) können diese Lerneinheit NICHT belegen. |
| Kurzbeschreibung | Baire category; Banach and Hilbert spaces, bounded linear operators; basic principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces; Fourier transform and applications. |
| Lernziel | Acquire a good degree of fluency with the fundamental concepts and tools belonging to the realm of linear Functional Analysis, with special emphasis on the geometric structure of Banach and Hilbert spaces, and on the basic properties of linear maps. |
| Literatur | We will be using the book Functional Analysis, Spectral Theory, and Applications by Manfred Einsiedler and Thomas Ward and available by SpringerLink. Other useful, and recommended references include the following: Lecture Notes on "Funktionalanalysis I" by Michael Struwe Haim Brezis. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. Elias M. Stein and Rami Shakarchi. Functional analysis (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011. Peter D. Lax. Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002. Walter Rudin. Functional analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. |