640:502 Real Analysis II (Spring, 2007)
Announcements:
- Final Exam: Tuesday, May 8, 4:00-7:00 (Hill 423)
Lecturer: Prof.
Roe Goodman
Text: (required) Gerald B. Foland, Real Analysis: Modern
Techniques and Their Applications (2nd ed.),
ISBN #0-471-31716-0,
Wiley-Interscience/John Wiley Sons, Inc., 1999.
This course is a continuation of 640:501 from Fall 2006. The
goal is to give an introduction to core topics in real and
functional analysis that every professional mathematician should know.
Homework Assignments: Here is the list of
homework problems.
Topics: The course will cover material from Chapters 4-8 of
Folland's book:
- Topological Spaces
Basic properties, compact spaces, Stone-Weierstrass theorem
- Introduction to Functional Analysis
Normed vector spaces, Hahn-Banach theorem, bounded linear
transformations, Closed graph and Open mapping theorem, applications
of Baire category theorem, Hilbert spaces, topological vector spaces,
weak and weak* convergence
- Lp Spaces
Integral inequalities, duality, bounded integral operators
- Introduction to Fourier analysis
Schwartz space, convolutions, Fourier transform and Fourier series, Plancherel
theorem, Poisson summation formula, Lp and pointwise
convergence of Fourier series
- Integration on Locally Compact Spaces
Continuous functions and Radon measures on locally compact spaces,
dual of C(X), vague convergence of measures
Here is a lecture-by-lecture
syllabus.
Grading: There are weekly graded homework assignments, an
in-class midterm exam (closed book) on March 7, and a final exam
(closed book) on May 8.
Roe Goodman /
goodman "at" math "dot" rutgers "dot" edu / Revised April 3, 2007