# ATML in Functional Analysis-II (2008)

Venue: |
BIM |

Dates: |
3-15 Nov |

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 Lectures**First 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 |

**Click here to download list of selected applicants**

How to reach |

NA