Course Archives    Theoretical Statistics and Mathematics Unit
Course: Functional Analysis
Instructor: Jaydeb Sarkar
Room: G25
Level: Postgraduate
Time: Currently offered
Syllabus
Past Exams


Syllabus: Normed linear spaces, Banach spaces. Bounded linear operators. Dual of a normed linear space. Hahn-Banach theorem, uniform boundedness principle, open mapping theorem, closed graph theorem. Computing the dual of wellknown Banach spaces. Weak and weak* topologies, Banach-Alaoglu Theorem. The double dual.

L^p spaces, Riesz representation theorem for the space C[0,1].

Hilbert spaces, adjoint operators, self-adjoint and normal operators, spectrum, spectral radius, analysis of the spectrum of a compact operator on a Banach space, spectral theorem for bounded self-adjoint operators.

Time permitting: reflexivity; spectral theorem for normal and unitary operators.

Suggested Texts :

1. W. Rudin, Real and complex analysis, McGraw-Hill (1987).

2. W. Rudin, Functional analysis, McGraw-Hill (1991).

3. J. B. Conway, A course in functional analysis, GTM (96), Springer (Indian reprint 2006).

4. K. Yosida, Functional analysis, Springer (Indian reprint 2004).

Evaluation:
Midterm Exam 40 marks
Assignment 10 marks
Final Exam 50 marks
Total 100 marks

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Past Exams
Midterm
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf 18.pdf
Solution
06.pdf 09.pdf 10.pdf 12.pdf 14.pdf 16.pdf
Semestral
04.pdf 09.pdf 10.pdf 12.pdf 16.pdf
Solution
04.pdf 09.pdf 10.pdf 12.pdf 16.pdf
Supplementary and Back Paper
04.pdf 10.pdf
Solution
10.pdf

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