Functional Analysis

This is an introductory Functional Analysis course at the PhD level. A basic outline of the syllabus for the

course can be found at this link under Math 824 .

Schedule: the class meets twice a week, Tuesday/Friday 3.30 pm - 4:55 pm, and extra problem sessions

every alternate Saturday starting 10 am.

Office Hours: Tuesday 1 - 3 pm.

There is no one book that will be linearly followed. However, almost all of the material covered in class

should be found in some guise in one of the following standard references:

1. P. Lax, Functional analysis. Pure and Applied Mathematics (New York). Wiley-Interscience, John Wiley &

Sons, New York, 2002. xx+580 pp.

2. K. Yosida, Functional analysis. Reprint of the sixth (1980) edition. Classics in Mathematics. Springer-Verlag,

Berlin, 1995. xii+501 pp.

3. Michael E. Taylor, Partial differential equations I. Basic theory. Second Edition, Applied Mathematical

Sciences, 115. Springer, New York, 2011. xxii+654 pp.

4*. M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol I - IV, Elsevier 1981.

(These are mainly for reference, but I cannot resist mentioning the books that built a foundation for

modern functional analysis).

Notes (to be updated after each class). The starred exercises are to be discussed in the Homework sessions.

Contact information:

Email: mathmukherjee@gmail.com or mukherjee@math.iitb.ac.in

Office: B1-B, Math Department (in the basement)

Miscellaneous ramblings:

1. There is no strict attendance policy, but it is strongly encouraged.

2. Regarding the homework, you are encouraged to discuss/collaborate with others, but you are responsible

solely for your final answer.

3. It is highly recommended that you consult other standard texts in the field, to appreciate different tastes

in selection of materials, or differing slants on the same material. For example, even in the three references

listed above, this difference is clearly perceptible.