FUNCTIONAL ANALYSIS (MTH 3106) Professor M.Shubin Fall 1996 Textbook: Essential Results of Functional Analysis , by Robert J. Zimmer The University of Chicago Press, Chicago, 1990 Office: 460 Lake Hall. Phone: Ext.5676 E-mail: shubin@neu.edu Class meets: Tuesday and Thursday 7:15 - 8:45 p.m., 544 Nightingale Hall Functional Analysis developed in 20th century from an idea to treat functions as points in an infinite-dimensional space. This idea allows a miraculously successful use of rich geometric intuition when dealing with functions. It proved to be extremely fruitful in applications to differential equations, harmonic analysis, ergodic theory, group representations, quantum mechanics, economics models. The aim of the course is to provide an introduction to essential results of Functional Analysis and some of its applications. The main prerequisite is the theory of Lebesgue integration, which is necessary mainly to understand examples, but at some moments is used in the theory itself. However the main abstract facts can be understood independently. Proofs of some important basic theorems about Hilbert and Banach spaces (e.g. Hahn-Banach Theorem and Open Mapping Theorem) will be omitted to allow more time for applications of the abstract technique. The principal topics to be covered are: - Basics on operators in Banach and Hilbert spaces and operator topologies.
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