Instructor: Demetrio Labate

• OFFICE:   PGH 694 
• EMAIL ADDRESS:   dlabate@math.uh.edu 
• HOMEPAGE:   http://www.math.uh.edu/~dlabate 

When and Where

• MEETING TIME:   MW 1-2:30,
• MEETING PLACE:   SR 140 
• OFFICE HOURS:   Mon: 12-1; Wed: 2:30-3:30 (or by appointment) 

Course Description:

This is the second part of the Functional Analysis sequence. The course covers the Spectral Theory for Compact and self-Adjoint operators, Unbounded Linear Operators in Hilbert Spaces, some applications from Harmonic Analysis and Mathematical physics (e.g., Pseudodifferential operators, Radon transform, applications). Additional topics will be identified based on the input from the students. . 

Textbook:

Introductory Functional Analysis with Applications, by Kreyszig, Wiley, 1989.  

Prerequisites:

Functional Analysis MA 7320, Real Analysis (MA 4331 or, better, MA 6320-6321) and Linear Algebra (MA 4377). The course and the textbook do not require a specific knowledge of measure theory, so that students don't need be too concerned if they lack that background. However, a solid background on elementary linear algebra (e.g., matrices, linear independence), analysis (e.g., convergence) and topology (e.g., open/closed sets) are necessary to successfully atten this class.

Course outline:

• Fundamental theorems for normed and Banach spaces
• Spectral theory of linear operators in normed spaces
• Spectral theory of compact operators in normed spaces
• Spectral theory of self-adjoint operators in normed spaces
• Applications and special topics (e.g., Radon transform, Pseudodifferential operators)

HOMEWORK:

• Homework 1: Sec 4.8: Ex 4,6; Sec 4.9: Ex 7,8; 4.12: 2,6 [Due: Feb 8]  
• Homework 2: Sec 4.13: Ex 8; Sec 7.1: Ex 4; Sec 7.2: Ex 2; Sec 7.3: Ex.4,6; Sec 7.4: Ex 4 [Due: Feb 23]  
• Homework 3: Sec 8.2: Ex 6; Sec 8.4: Ex 4,5,6; Sec 8.6: Ex 6,7 [Due: Mar 23]  
• Homework 4:

Tests and Exam Dates:

The dates for the teo midterm exams are (tentatively) Wed Mar 2 and Mon April 4.

Grading:

Grades will be based on homework assignments counting 40% towards the final grade, on two midterm exams counting 30% towards the final grade and one final counting 30% towards the final grade. 

The grade will be determined according to a set point scale: 90%-100%: A, 80%-89%: B, 70%-79%: C, 60-69% D; F is less than 60% (+ and - will also be used).