Instructor: Demetrio Labate

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

When and Where

• MEETING TIME:   MWF 11-12
• MEETING PLACE:  C 102 
• OFFICE HOURS:   MF 12-1; or by appointment 

Course Description:

This is the second semester of a two-semester sequence in graduate real analysis. After covering measure theory and Lebesgue integration during the first semester, this semester be devoted mostly to the following topics: Lp spacse and Hilbert spaces, convolutions, Fourier transform and Fourier series, differentiation. . 

Textbook:

Lebesgue Integration on Euclidean Space (Revised Ed.), by Frank Jones. Publisher: Jones and Bartlett Books in Mathematics, 2000. Additional reading material will be provided by the instructor.

• Material on Lp spaces: Chapter on Lp spaces

Prerequisites:

MATH 6320 or an equivalent course in measure theory and Lebesgue integration.

Course outline:

• Abstract measures
• Lp spaces and Hilbert spaces
• Convolution
• Fourier transform and Fourier series
• Differentiation

HOMEWORK:

• Homework 1: HW1 assignment - [Due: 1/28/2013]  

• Homework 2: HW2 assignment - [Due: 2/13/2013]  

• Homework 3: HW3 assignment - [Due: 3/18/2013]  

• Homework 3: HW4 assignment - [Due: 4/1/2013]  

• Homework 3: HW5 assignment - [Due: 4/22/2013]  

Tests and Exam Dates:

The dates for the two midterm exams are Wed Feb 27 and Mon Apr 8. The final exam will be a take-home exam.

• FINAL EXAM: Take-home Exam - [Due: FRI, May 3, 8:05AM]  

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).