Functional Analysis - Core

Venue: Chern Lecture Hall

Class Timings: Tuesdays and Fridays from 11:30 PM - 1:00 PM

First Meeting: 7 January 2025

Course Syllabus: 

• Banach spaces : Banach spaces, dual space, Hahn-Banach theorem.
  
• Baire category theorem : Baire category theorem and applications (open mapping, closed graph and uniform boundedness theorems).
•  Weak* topologies: Weak and Weak* topologies, Banach Alaoglu theorem separable, reflexive and locally convex topological vector spaces.
• Hilbert spaces: Hilbert spaces, projection theorem, Riesz representation theorem, adjoint operators.
• Generalized functions and elements of harmonic analysis
• Compact operators: Spectral theory for compact operators.

Course Format: Reading

Course Outcome:

• Develop a comprehensive understanding of core concepts in functional analysis, including Banach spaces, Hilbert spaces, and generalized function spaces.
  
• Apply foundational theorems of functional analysis to solve advanced theoretical problems.
  
• Develop an understanding of the spectral properties of compact operators.