Venue: | Bhaskaracharya Pratishthana |
Dates: | 3-15 Nov, 2008 |
Convener(s) | Speakers, Syllabus and Time table | Applicants/Participants |
Name | A. Mangasuli | V. M. Sholapurkar |
Mailing Address |
Bhaskaracharya Pratishthana |
S. P. College |
Advanced Training School in Mathematics for Lecturers (ATML) in Functional Analysis-II is being organised in Pune at Bhaskaracharya Institute of Mathematicsin November 2008 on behalf of NBHM.
Members of the Local Organising Committee
V. M. Sholapurkar, S. P. College, Pune 411030 (Convener)\\ A. Mangasuli, BIM, Pune (Convener)\\ C. S. Inamdar, BIM, Pune (Custodian, BIM) \\ S. A. Katre, Univ. of Pune (Trustee, BIM)
Resource Persons:
Speakers
Dr. H. Bhate | Univ. of Pune | hbhate at math.unipune.ernet.in |
Dr. Sameer Chavan | HRI, Allhabad | chavansameer at mri.ernet.in |
Dr. Anandateertha Mangasuli | BIM, Pune | anandateertha at gmail.com |
Dr. V. M. Sholapurkar | S.P. College, Pune | deepaksholapurkar at yahoo.com |
Unity of Mathematics Lectures:
Prof. G. Misra, I.I.Sc. Bangalore
Bergman Kernels
Dipendra Prasad, TIFR, Bombay
Harmonic Analysis on groups
Course Associate
1. Geetanjali Phatak
2. Pratul Gadagkar
Syllabus
(a) Review of Linear Algebra : Spectral Theorem for Normal Operators on Finite Dimensional Inner Product Spaces.
(b) Hilbert Spaces :
i. Examples of Hilbert Spaces.
ii. Cauchy-Schwarz Inequality, Pythagoras Theorem, Parallelogram
Law, orthogonal complement, orthogonal projection and orthonor- mal basis
iii. Reisz Representation Theorem
iv. Direct Sum of Hilbert Spaces
(c) Operators on Hilbert Spaces :
i. Examples of Operators : Unilateral and bilateral shift, weighted shifts, multiplication operator, integral operator, Fourier transform
ii. Adjoint of an operator, invariant and reducing subspaces
iii. Special classes of operators: finite rank operators, compact operators, isometries, projections, unitary operators, self adjoint operators, normal operators.
iv. Spectrum of an operator : Spectral parts, properties of spectra, computation of spectra of some operators.
v. Properties of spectrum of a compact operator and spectrum of a normal operator
vi. Spectral Theorem for compact normal operators on Hilbert Spaces vii. Applications of Spectral Theorem.
References :
(a) John. B. Conway, A Course in Function Analysis, 2nd edition, (GTM 96), New York, Springer, 1990
(b) Paul R. Halmos, A Hilbert Space Problem Book, 2nd edition, New York, Springer, 1982
(c) Balmohan V. Limaye, Functional Analysis, New Delhi : Wiley Eastern Ltd, 1981
Speakers
[A]A. Mangasuli - Spectral Theorem for Normal Operators on Finite Dimensional Inner Product Spaces
[B]H. Bhate - Hilbert Spaces & Fourier analysis on finite groups
[C]V. Sholapurkar - Bounded operators on Hilbert Spaces
[D]S. Chavan - Spectral Theorem for bounded normal operators on Hilbert Spaces
[UM-1,2,3] G. Misra - Bergman Kernels
[UM-4] Dipendra Prasad - Harmonic Analysis on Groups
Schedule of LecturesFirst Week
Day | 0930 to 1100 | 1130 to 1300 | 1445 to 1645 |
I | A | B | Tut (A) |
II | A | B | Tut (B) |
III | A | C | Tut (A) |
IV | A | B | Tut (B) |
V | C | D | Tut (C) |
VI | C | B | Tut (D) |
Second Week
Day | 0930 to 1100 | 1130 to 1300 | 1430 to 1600 | 1600 to 1730 |
I | B | D | Tut (B) | |
II | C | D | Tut (C) | |
III | C | D | Tut (D) upto 1530 | UM-1 |
V | UM-3 | D | D | |
VI | UM-4 | D | Tut (D) |
Selected Applicants |
No. | Name of the Student | Name of Institute | Place |
1. | P. Sam Johnson | National Institute of Technology, Surathkal | Karnataka |
2. | V. Murugan | National Institute of Technology, Surathkal | Karnataka |
3. | Dr. D. Sukumar | National Institute of Technology, Surathkal | Karnataka |
4. | Shireen | Banaras Hindu University | Varanasi |
5. | Mahesh Sahebrao Wavare | Nutan Mahavidyalaya, Sailu | Parbhani |
6. | G Sankara Raju Kosuru | Indian Institute of Technology, Madras | Chennai |
7. | Vinay Arora | SSG Panjab University Regional Centre | Bajwara |
8. | Faiza Shujat | Aligarh Muslim University | Aligarh |
9. | Sabiha Tabassum | Aligarh Muslim University | Aligarh |
10. | Mr. J. Maria Joseph | St. Joseph’s College (Autonomous) | Trichy |
11. | John Paul M. | Dept. of Math. Bharathidasan University | Tiruchirappalli |
12. | Miss Nargis Jamal | Aligarh Muslim University | Aligarh |
13. | D. Jayaseelan Samuel | Madras Christian College, Tambaram | Chennai |
14. | Dr. M. Marudai | Bharathidasan University | Tiruchirappalli |
15. | U. Karuppiah | St. Joseph’s College (Autonomous) | Trichy |
16. | Sankara Narayanan M. | The American College Madurai | Madurai |
17. | K. Premakumari | Pachaiyappa’s College | Chennai |
18. | Khan Nasreen Lukman | Abeda Inamdar Sr. College | Pune |
19. | Tejasvi Rajendra Shinde | Abeda Inamdar Sr. College | Pune |
20. | Sonali Vishnu Mandavkar | Abeda Inamdar Sr. College | Pune |
21. | Shraddha Ramakant Natu | Abeda Inamdar Sr. College | Pune |
22. | Bhagyashri Pramod Kadam | Prof. Ramkrushna More College | Pune |
23. | Ishrat Jahan MD. Haroon Ansari | Abeda Inamdar Sr. College | Pune |
24. | Sanjay Kumar Thakur | Science College | Kokrajhar |
25. | Debasisha Mishra | Dept. of Math. IIT | Madras |
26. | Franklin V. | Bishop Heber College | Trichy |
27. | Dr. Rajesh Kumar | Pacchunga University College Aizawal | Mizoram |
28. | Dr. Agrawal Sushma Narayan Das | University of Madaras | Chennai |
29. | G. Ramesh | Dept. of Math. IIT Madras | Chennai |
30. | Vaishali A. Kolhatkar | Sinhgad College of Scie. | Vadgaon (BK) Pune |
How to reach |