The goal of this school is to expose early graduate students to harmonic analysis. In one direction, classical harmonic analysis will be developed, covering Plancherel theorem and Paley-Wiener theorems for the Euclidean Fourier transform and then introducing the participants to the theory of Hilbert transform. In the other direction, representation theory of compact groups , matrix groups, their Lie algebras, representations etc will be covered in detail thus giving a taste of different aspects of basic harmonic analysis.
Syllabus:
|
Name of the Speaker with affiliation |
No. of Lectures (each of 1 ½ hrs) |
Detailed Syllabus |
|
Prof. Sanjay P. K (NIT, Calicut) |
6 |
Review of functional analysis (without proofs), interpolation theorems (Riesz-Thorin, Marcinkiewicz, Stein's etc) |
|
Prof E. K. Narayanan (IISc, Bangalore) |
6 |
C* algebras, Gelfand-Naimark Theorem, spectral theorem for self adjoint operators. |
|
Prof Parasar Mohanty (IIT Kanpur) |
6 |
Fourier transform on the real line, Plancherel, Paley-Wiener theorems, Hilbert transform on the real line. |
|
Prof Swagato Ray (ISI, Kolkata) |
6 |
Fourier series, Plancherel theorem, Poisson integrals and harmonic functions in the disc, Hilbert transform, summability results |
|
Prof S. Thangavelu (IISc, Bangalore) |
6 |
Matrix groups, exponential map, Lie algebras, representations of SU(2) etc. |
|
Prof Rudra Sarkar (ISI, Kolkata) |
6 |
Topological groups, unitary representations, Gelfand-Raikov theorem, Peter-Weyl theorem. |
References:
- Interpolation of operators and Singular Integrals by C. Sadosky
- Introduction to Fourier Analysis on Euclidean spaces by E. M Stein and G. Weiss
- A course in Abstract harmonic analysis by G. B. Folland
- First course in representation theory and Linear Lie groups by B. Bagchi, S. Madan, A. Sitaram and U. B. Tewari
Time-Table :
|
Day |
Date |
Lecture 1 9.30–11.00 |
Tea 11.00–11.30 |
Lecturer 2 11.30–1.00 |
Lunch 1.00–2.30 |
Tutorial 2.30–3.30 |
Tea 3.30-4.00 |
Tutorial 4.00-5.00 |
Snacks 5.00-5.30 |
|
|
|
name of the speaker |
|
name of the speaker |
|
name of the speaker/ tutor |
|
|
|
|
Mon |
05.12.2016 |
SPK |
|
EKN |
|
SPK |
|
JJ |
|
|
Tues |
06.12.2016 |
SPK |
|
EKN |
|
JJ |
|
EKN |
|
|
Wed |
07.12.2016 |
SPK |
|
EKN |
|
SPK |
|
JJ |
|
|
Thu |
08.12.2016 |
SPK |
|
EKN |
|
JJ |
|
EKN |
|
|
Fri |
09.12.2016 |
SPK |
|
EKN |
|
SPK |
|
JJ |
|
|
Sat |
10.12.2016 |
SPK |
|
EKN |
|
JJ |
|
EKN |
|
|
SUNDAY |
|||||||||
|
Mon |
12.12.2016 |
SR |
|
RS |
|
JJ |
|
MB |
|
|
Tues |
13.12.2016 |
SR |
|
RS |
|
MB |
|
JJ |
|
|
Wed |
14.12.2016 |
SR |
|
RS |
|
JJ |
|
MB |
|
|
Thu |
15.12.2016 |
SR |
|
RS |
|
MB |
|
JJ |
|
|
Fri |
16.12.2016 |
SR |
|
RS |
|
JJ |
|
MB |
|
|
Sat |
17.12.2016 |
SR |
|
RS |
|
MB |
|
JJ |
|
|
SUNDAY |
|||||||||
|
Mon |
19.12.2016 |
PM |
|
ST |
|
RK |
|
AG |
|
|
Tues |
20.12.2016 |
PM |
|
ST |
|
AG |
|
RK |
|
|
Wed |
21.12.2016 |
PM |
|
ST |
|
RK |
|
AG |
|
|
Thu |
22.12.2016 |
PM |
|
ST |
|
AG |
|
RK |
|
|
Fri |
23.12.2016 |
PM |
|
ST |
|
RK |
|
AG |
|
|
Sat |
24.12.2016 |
PM |
|
ST |
|
AG |
|
RK |
|
Resource Persons:
|
S. No. |
Name |
Affiliation |
|
1 |
Prof. Sanjay P. K (SPK) |
NIT, Calicut |
|
2 |
Prof E. K. Narayanan (EKN) |
IISc, Bangalore |
|
3 |
Prof Parasar Mohanty (PM) |
IIT Kanpur |
|
4 |
Prof Swagato Ray (SR) |
ISI, Kolkata |
|
5 |
Prof S. Thangavelu (ST) |
IISc, Bangalore |
|
6 |
Prof Rudra Sarkar (RS) |
ISI, Kolkata |
Tutorial Assistants:
|
S. No. |
Name |
Affiliation |
|
1 |
Jis Joseph (JJ) |
Research Scholar, IISc, Bangalore |
|
2 |
Mithun Bhowmik (MB) |
Research Scholar, ISI Kolkata |
|
3 |
Rakesh Kumar (RK) |
Research Scholar, IISc, Bangalore |
|
4 |
Abhisek Ghosh (AG) |
Research Scholar |