Prof. G. Ramesh

Professor, Department of Mathematics, Indian Institute of Technology Hyderabad

Lecture Notes & Course Materials

Notes on Weak Topologies
Lecture notes prepared for AFS-II, held at KSOM, Calicut, from 6 June 2016 to 1 July 2016.
Spectral Theorem for Compact Self-adjoint Operators
Lecture notes given at NITK Surathkal during the workshop Spectral Analysis and Applications, 14–16 February 2013.
Notes on Banach Algebras
A first version of lecture notes on Banach algebras.

Lecture Slides

Laplace Transforms
Lecture slides covering the following sessions:
Fourier Transforms
Lecture slides covering Fourier transforms.

NPTEL Operator Theory Lectures

Operator Theory — NPTEL Video Lectures
Selected NPTEL lectures covering operator theory, spectral theory, spectral mapping, and spectral measures.
  1. Weeks 1–10 (Lectures 1–46)
  2. Spectral theorem for self-adjoint operators: Multiplication form (Lecture 47, Week 11)
  3. Spectral mapping theorem for normal operators: Polynomials (Lecture 48, Week 11)
  4. Spectral mapping theorem for normal operators: Continuous functions (Lecture 49, Week 12)
  5. Spectral theorem for normal operators: Multiplication form (Lecture 50, Week 12)
  6. Spectral measure (Lecture 51, Week 12)
  7. Spectral measures and representations (Lecture 52, Week 12)
  8. Spectral theorem for normal operators (Lecture 53, Week 12)