ATML in Functional Analysis-II (2008)

Venue: BIM
Dates: 3-15 Nov


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name A. Mangasuli V. M. Sholapurkar
Mailing Address

Bhaskaracharya Pratishthana
56/14, Erandavane, Damle Path,
Off Law College Road, Pune - 411 004.

 S. P. College
  Pune 411030

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)


Speakers and Syllabus 

Resource Persons:

Dr. H. Bhate Univ. of Pune hbhate at
Dr. Sameer Chavan HRI, Allhabad chavansameer at
Dr. Anandateertha Mangasuli  BIM, Pune anandateertha at
Dr. V. M. Sholapurkar S.P. College, Pune  deepaksholapurkar at

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


(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


[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

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