MATH 7132: Functional Analysis
Spring 1999. University of Colorado at Denver

PREREQUISITE:
MATH 6131: Introduction to Real Analysis, or with instructor's approval

HOURS: TR 4-5:15 pm, CU (Dravo) 641.

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: Wed 3pm - 6pm (or by appointment)
WWW: http://math.ucdenver.edu/~aknyazev

Students are invited to participate in the interactive DISCUSSION.

TEXTBOOKS:
Required: Introduction to Hilbert Spaces : With Applications by Lokenath Debnath, Piotr Mikusinski,
Hardcover - 522 pages 2 Ed edition (November 1998) Academic Pr; ISBN: 0122084365
Optional:  Integral, Measure, and Derivative by Georgi. Shilov,  B. L. Gurevich , and
Richard A. Silverman (Translator), ISBN:  0486635198,  Publisher  Dover Publications.

SUBJECT:
Linear metric and normed spaces, spaces of functions, linear operators, compact operators, elements of spectral theory.

CONTENTS:
The class will follow the outline below, touching on each major topic in a depth that will be determined by the pace of the class.

• Ch 1. Normed Vector Spaces.
• Ch 2. The Lebesgue Integral (a reading assignment).
• Ch 3. Hilbert Spaces.
• Ch 4. Linear Operators on Hilbert Spaces
• Ch 5-9. Applications (brief)

LINKS: 

• Real Analysis by Bert G. Wachsmuth,
• Measure Theory and Functional Analysis by Vitali Liskevich,
• Advanced Calculus by Ian Craw,
• Hilbert Space Methods for Partial Differential Equations by Ralph Showalter.
• Monotone Operators in Banach Space and Nonlinear Partial Differential Equations by Ralph Showalter.
• Complex/Functional Analysis by Douglas N. Arnold
• Problems