Syllabus for Math 633, Functional Analysis
Fall Semester, 2015
Instructor:
Office:
Office Hours:
Homepage:
Eric Weber
Email:
Carver Hall 454
Phone:
MWF 1:30-2:30pm, or by appointment
http://www.public.iastate.edu/∼esweber
esweber@iastate.edu
294-8151
Class Homepage: http://www.public.iastate.edu/∼esweber/Math633/ This page will contain a copy of this syllabus, a detailed calendar of the semester’s material, links to other
relevant information, and assignments as they are given. There is also a Blackboard course
that I will use for posting grades and information.
Course Description: MATH 633. Functional Analysis. (3-0) Cr. 3. Alt. F., offered
odd-numbered years. Prereq: MATH 515 Fundamental theory of normed linear spaces and
algebras, such as topology and continuity, duality and spectral theory, emphasizing aspects
that provide a framework for the study of boundary-value problems, eigenvalue problems,
harmonic analysis, analytic function theory, and modern operator theory.
Learning Outcomes: The student will understand the following concepts:
(1) Hilbert and Banach spaces, Banach algebras, C∗ -algebras
(2) Existence of orthonormal bases, projections, complemented subspaces
(3) bounded linear operators
(4) Banach space valued analytic functions
(5) the spectrum of an operator, the spectrum of an algebra
(6) the Gelfand transform
(7) the Spectral Theorem of Normal operators and Compact operators
(8) Reproducing Kernel Hilbert Spaces
(9) the Hardy space of analytic functions
(10) de Branges-Rovnyak spaces
(11) boundary behavior of analytic functions on the disc
Textbook: There is no official textbook for the course. I will use the following three books
as references, and I have requested these books to be reserved in the library:
(1) Functional Analysis, Walter Rudin, McGraw Hill, ISBN: 0070542368
(2) Functional Analysis: a primer, Lawrence W. Baggett, Marcel Dekker, ISBN: 0824785983
(3) Functional Analysis, Peter Lax, Wiley, ISBN: 0471556041
If you wish to purchase a book for this course, I recommend one of these three.
The following books are available in the library (though may be checked out), and can be
used for your own reference as an alternative to buying a book:
(1) A Course in Functional Analysis, John B. Conway
(2) Functional Analysis, Kōsaku Yosida
(3) Functional Analysis, Elias Stein and Rami Shakarchi
(4) Beginning Functional Analysis, Karen Saxe
(5) Elementary Functional Analysis, Barbara MacCluer
(6) Introductory Functional Analysis with Applications, Erwin Kreyszig
(7) Elements of Functional Analysis, Arlen Brown and Carl Pearcy
(8) Introduction to Functional Analysis, Angus Taylor and David Lay
(9) An Introduction to Functional Analysis, Charles Swartz
2
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
A First Course in Functional Analysis, S. David Promislow
Functional Analysis, Carl DeVito
Foundations of Functional Analysis, S. Ponnusamy
Functional Analysis, S. Kegavan
Functional Analysis, Pawan Jain and Om Ahuja
Functional Analysis, Erdoǧan Su̧hubi
Functional Analysis, Dzung Minh Ha
A First Course in Functional Analysis, D. Somasundaram
Grading: Grade percentages break down as follows:
Assignment:
Homework
Presentation
Final
Percentage:
40%
30%
30%
Date:
Weekly
Dec. 1-11
Dec. 14
The following overall percentages will assure you of the associated letter grade: 90%: A;
80%: B; 70%: C; 60%: D. There may be a curve at the end of the semester.
Exams: There will be one final exam. The format of the exam may be in class, take home,
or consist of both. I expect that on any take home exam, no collaboration with classmates
will occur.
Homework: Homework will be assigned sporadically, most likely once a week, though
sometime more frequently, sometimes less. The assignment is due one week after being
assigned. Each individual assignment is worth two points; one point will be awarded for
turning the assignment in on time, and a second point for correctly solving the problem. I
expect you to turn in a first attempt on time; however, the emphasis here is on correctness
of your work. Thus, you will be able to make revisions and turn in the problem a second
time to earn a second point, if correct. Every submission must contain your name and the
date the problem was originally assigned.
Presentations: Each student will give an in-class presentation of relevant course material.
Details, such as topics and dates for individuals, will be determined at a later date.
Academic Dishonesty: Academic dishonesty is very serious. Any case of cheating, plagiarism, etc, will be handled as described in the Student Disciplinary Regulations.
Disability Policy: Please address any special needs or special accommodations with me at
the beginning of the semester or as soon as you become aware of your needs. Those seeking
accommodations based on disabilities should obtain a Student Academic Accommodation
Request (SAAR) form from the Disability Resources (DR) office (515-294-6624). DR is
located on the main floor of the Student Services Building, Room 1076.
Copyright: Please note that all written and web materials for this course have an implied
copyright. In particular, you can photocopy or download for your own use, but you may not
reproduce them for others.