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401-3461-00L  Functional Analysis I

SemesterHerbstsemester 2019
DozierendeM. Struwe
Periodizitätjährlich wiederkehrende Veranstaltung
LehrspracheEnglisch
KommentarHöchstens eines der drei Bachelor-Kernfächer
401-3461-00L Funktionalanalysis I / Functional Analysis I
401-3531-00L Differentialgeometrie I / Differential Geometry I
401-3601-00L Wahrscheinlichkeitstheorie / Probability Theory
ist im Master-Studiengang Mathematik anrechenbar.


KurzbeschreibungBaire 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.
LernzielAcquire 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.
LiteraturWe will be using the Lecture Notes on

"Funktionalanalysis I" by Michael Struwe.

Other useful, and recommended references include the following books:

Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011.

Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017.

Peter D. Lax: "Functional analysis". Pure and Applied Mathematics (New York). Wiley-Interscience [John Wiley & Sons], New York, 2002.

Elias M. Stein and Rami Shakarchi: "Functional analysis" (volume 4 of Princeton Lectures in Analysis). Princeton University Press, Princeton, NJ, 2011.

Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.

Dirk Werner, "Funktionalanalysis". Springer-Lehrbuch, 8. Auflage. Springer, 2018
Voraussetzungen / BesonderesSolid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH (most remarkably: fluency with measure theory, Lebesgue integration and L^p spaces).