By Prof. G. Ramesh |
IIT Hyderabad

Learners enrolled: 316

About the course:

In this course, we aim to study the spectral theory of normal operators and continuous functional calculus. We begin with the introduction of Hilbert space and study bounded operators on these spaces. More often we compare the results on operators with operators on finite-dimensional Hilbert spaces (or matrices). In this way, we study the spectrum and its properties, spectral theorem for compact normal operators which is a generalization of finite-dimensional operators. The further generalization is the spectral theorem for normal operators.

PREREQUISITES : Functional Analysis

In this course, we aim to study the spectral theory of normal operators and continuous functional calculus. We begin with the introduction of Hilbert space and study bounded operators on these spaces. More often we compare the results on operators with operators on finite-dimensional Hilbert spaces (or matrices). In this way, we study the spectrum and its properties, spectral theorem for compact normal operators which is a generalization of finite-dimensional operators. The further generalization is the spectral theorem for normal operators.

PREREQUISITES : Functional Analysis

INTENDED AUDIENCE : M. Sc Mathematics II Year students and Ph. D first year students

1. **Conway, John B**. A course in functional analysis. Second edition. Graduate Texts in Mathematics, 96. Springer-Verlag, New York, 1990. xvi+399 pp.

2. W. Rudin, {\it Functional analysis}, second edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991.

3. **Bhatia, Rajendra** Notes on functional analysis. Texts and Readings in Mathematics, 50. Hindustan Book Agency, New Delhi, 2009. x+237 pp. ISBN: 978-81-85931-89-0

4. **Gohberg, Israel; Goldberg, Seymour; Kaashoek, Marinus A**. Basic classes of linear operators. Birkhäuser Verlag, Basel, 2003. xviii+423 pp. ISBN: 3-7643-6930-2

5. **Bachman, George; Narici, Lawrence** Functional analysis. Reprint of the 1966 original. Dover Publications, Inc., Mineola, NY, 2000. xii+532 pp. ISBN: 0-486-40251-7

6. **Pedersen, Gert K**. Analysis now. Graduate Texts in Mathematics, 118. Springer Verlag, New York, 1989. xiv+277 pp.

Dr. G. Ramesh completed his Ph. D (Operator Theory) from IIT Madras in 2008 and did Post Doctoral studies at ISI Bangalore, Bengaluru during 2009-2010 and worked as an Assistant Professor at Hyderabad University till June 2011. In 2011 July, he joined as an assistant professor in IUT Hyderabad. Currently, he is an Associate Professor at IIT Hyderabad. His area of specialization is Functional Analysis and Operator Theory.

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: **30 October 2022** Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Hyderabad. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

## DOWNLOAD APP

## FOLLOW US