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Course Descriptions

16:640:510 - Topics in Analysis

Avy Soffer

Subtitle:

Introduction to Spectral Theory

Course Description:

This is an introductory course to those interested in the aspects of spectral theory and its applications. It may be of interest to those who work in PDE, Math-Phys, Analytic Number Theory and Analysis on Manifolds.

I begin with a review of the basics of Hilbert spaces and then discuss the theory of linear operators on Hilbert spaces.

The needed results from Functional Analysis will be detailed in class.  Topics included then are the spectral theorem and its applications, compact operators, trace class and Hilbert Schmidt operators, unbounded self-adjoint operators.

Text:

Books: Reed & Simon , Functional Analysis I, Operator Theory part 4, by Simon.

Prerequisites:

Real Analysis, Complex Analysis, Linear Algebra

 

Sections Taught This Semester:

For more information on current instructors and sections for this course, please click HERE .

For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530