401-3461-00L Functional Analysis I
| Semester | Herbstsemester 2024 |
| Dozierende | M. Burger |
| Periodizität | jährlich wiederkehrende Veranstaltung |
| Lehrsprache | Englisch |
| Kommentar | Höchstens 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. Die Kategoriezuordnung können Sie in diesem Fall nicht selber in myStudies vornehmen, sondern Sie müssen sich dazu nach dem Verfügen des Prüfungsresultates an das Studiensekretariat (www.math.ethz.ch/studiensekretariat) wenden. |
| 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 graph theorem; spectral theory of self-adjoint operators in Hilbert spaces. Basics of Sobolev spaces. | |||||||||||||||
| 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 | Recommended references include the following: Michael Struwe: "Funktionalanalysis I" (Skript available at https://people.math.ethz.ch/~struwe/Skripten/FA-I-2019.pdf) Haim Brezis: "Functional analysis, Sobolev spaces and partial differential equations". Springer, 2011. 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. Manfred Einsiedler and Thomas Ward: "Functional Analysis, Spectral Theory, and Applications", Graduate Text in Mathematics 276. Springer, 2017. Walter Rudin: "Functional analysis". International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991. | |||||||||||||||
| Voraussetzungen / Besonderes | Solid background on the content of all Mathematics courses of the first two years of the undergraduate curriculum at ETH.Most importantly: fluency with point set topology and measure theory, in part. Lebesgue integration and L^p spaces. | |||||||||||||||
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