Course Archives    Theoretical Statistics and Mathematics Unit

Course: Abstract Harmonic Analysis Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus: [Prerequisite: Fourier Analysis] Banach Algebras and spectral theory: Banach Algebras, Gelfand theory, spectral theorem. Generalities on Locally compact groups: Haar measure, modular function and convolution. Basic representation theory: Unitary representation of groups, Schur’s lemma, Positive definite functions and GNS construction. Analysis on Locally compact abelian groups: Fourier transform and the dual group, Pontrajin Duality, Bochner’s theorem, Plancherel theorem. If time permits: Peter Weyl theorem and analysis on compact groups. ADDITIONAL TOPICS FROM: Social choice, Voting and ranking Mechanisms, Arrow’s impossibility theorem; Repeated games; Random-turn games; Fair-design; Reference Texts: 1. A course in abstract Harmonic Analysis- G. B. Folland. 2. Principles of Harmonic Analysis- A. Deitmar, S. Echterhoff. 3. Fourier Analysis on groups- W. Rudin. 4. Fourier Analysis on Number Fields- Dinakar Ramakrishnan, Robert J. Valenza. Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]