Instructor. Michael Anderson, Math 4-110.
E-mail: anderson@math.sunysb.edu, Phone: 632-8269.
Lectures: MF: 11:20-12:40, in Math 4-130.

Office Hours. TuWTh 1-2pm, and by appointment.

Course Description. This is a basic course in functional analysis centered on the spectral theorem for bounded and unbounded operators in Hilbert and Banach spaces. Having developed this, we will then focus on several applications to linear and possibly some aspects of non-linear PDE.

Topics to be discussed include:

• Review and examples of Hilbert and Banach spaces
• Spectral theorem for compact and bounded operators, examples
• Spectral theorem for unbounded operators, examples
• Selected applications to linear and non-linear PDE

Prerequisites: The basic core course curriculum.

Texts. There are no texts that will be required for the course per se. At least for the first half of the semester, the main reference is:

• M. Reed and B. Simon, Methods of Modern Mathematical Physics, vol I: Functional Analysis, Academic Press, (1980).

Other texts you might like to consult include:


• N. Akhiezer and I. Glazman, Theory of linear operators in Hilbert space, Dover Publ., (1993).
• N. Dunford and J. Schwartz, Linear Operators, Part I. General Theory, Wiley and Sons, (1988)
• K. Yosida, Functional Analysis, 6th Edition, Springer Verlag, (1980)
• W. Rudin, Functional Analysis, McGraw-Hill, (1973)
• F. Riesz and B. Sz.-Nagy, Functional Analysis, Ungar Publishing, New York, (1972).

Assignments and Grading: There may be occasional homework assignments or exercises, not necessarily individually graded. It may also be possible to do some class presentations of some material. Besides this, the class grade will be based on class participation.

Americans with Disability Act. If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disabled Student Services in ECC (Educational Communications Center) Building, Room 128, (631) 632-6748. They will determine with you what accomodations are necessary and appropriate. All information and documentation is confidential.
Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disabled Student Services. For procedures and information, go the following website: http://www.ehs.sunysb.edu/fire/disabilities/asp, here