MAT 551: Real Analysis III
Department of Mathematics
SUNY at Stony Brook
- Michael Reed and Barry Simon, Method
of Modern Mathematical Physics, v. 1 & 2, Academic Press, 1972
You can also consult many other good textbooks and monographs on
- Daryl Geller, A
first graduate course in real analysis. Parts I-II Solutions Custom Publishing (can be
ordered from the campus bookstore)
- N. Akhiezer and I. Glazman, Theory of linear operators in Hilbert
space. Dover Publications, Inc., New York, 1993
- N. Dunford and J. Schwartz, Linear operators. Part I.
General theory. John Wiley & Sons, Inc., New
- K. Iosida, Functional analysis. 6th ed.,
- W. Rudin, Functional analysis, 2nd ed., McGraw-Hill,
Inc., New York, 1991
Schedule: TuTh 12:50 - 2:10 PHYSICS P125.
Instructor: Leon Takhtajan, Math Tower 5-116, Phone:
632-8290, email: email@example.com.
Prerequisites: The basic core courses curriculum.
- Review of Banach, Hilbert and locally convex vector spaces
- Distributions and Fourier transforms, Hermite functions
- Bounded and compact operators, the spectral theorem
- Unbounded operators, symmetric and self-adjoint operators,
spectral theorem, examples
- Stone theorem, the Trotter product formula
- Commutative Banach algebras, C*-algebras
Howework & Exams: Homework will be posted on the web
with problems varying from routine to more challenging. Course grades
be based on these problems, class participation, the midterm exam and
- Review of Real Analysis I and II.
- HW 1 Ch. 2 in Reed-Simon, v.1:
- Introduction to locally convex topological vector
spaces and theory of distributions.
- HW 2 Ch. 5 in Reed-Simon, v.1:
- Notes on Fourier Transform.
- HW 3 Ch. 6 in Reed-Simon, v.1:
- Notes on bounded and compact operators.
- Notes on trace class and Hilbert-Schmidt
- Notes on spectral theorem.
- Notes on unbounded operators.
DSS advisory. If you have a physical,
medical, or learning disability that may affect your ability to carry
the assigned course work, please contact the office of Disabled Student
Services (DSS), Humanities Building, room 133, telephone 632-6748/TDGD.
DSS will review your concerns and determine what accommodations may be
necessary and appropriate. All information and documentation of