Curriculum and Syllabi - Indian Institute of Technology Bhubaneswar

Texts:1. M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002References:1. M. Pollicott and M. Yuri, Dynamical systems and Ergodic Theory, Cambridge University Press, 1998(xxvii) Abstract Harmonic Analysis (MA6018)):3-1-0: 4 Credits Prerequisite: Topology, AlgebraTopological groups, locally compact groups, Haar measure. Modular function, convolutions,homogenous spaces , unitary representations, Gelfand-Raikov theoremFunctions of positive type,GNS construction, Potrjagin dulaity, Bochner's theorem, Induced representations, Mackey'simpritivity theorem.Texts:1. G. B. Folland: A course in Abstract Harmonic Analysis. Studies in Advanced mathematics, CRC press,1995.2. E. Hewitt and K. Ross: Abstract Harmonic Analysis , Vol 1, Springer 1979References:3. S. A. Gaal. Linear Analysis and Representation theory. Springer(xxviii) Fourier Analysis (MA6019):3-1-0: 4 Credits Prerequisite: Real AnalysisBasic Properties of Fourier Series: Uniqueness of Fourier Series, Convolutions, Cesaro and AbelSummability, Fejer's theorem, Poisson Kernel and Dirichlet problem in the unit disc. Mean squareConvergence, Example of Continuous functions with divergent Fourier series. Distributions andFourier Transforms: Calculus of Distributions, Schwartz class of rapidly decreasing functions, Fouriertransforms of rapidly decreasing functions, Riemann Lebesgue lemma, Fourier Inversion Theorem,Fourier transforms of Gaussians. Tempered Distributions: Fourier transforms of tempereddistributions, Convolutions, Applications to PDEs (Laplace, Heat and Wave Equations), Schrodinger-Equation and Uncertainty principle. Paley-Wienner Theorems, Poisson Summ-ation Formula: RadialFourier transforms and Bessel's functions. Hermite functions.Optional Topics: Applications to PDEs, Wavelets and X-ray tomography.Applications to NumberTheory.Texts:1. R. Strichartz, A Guide to Distributions and Fourier Transforms, CRC Press.2. E.M. Stein and R. Shakarchi, Fourier Analysis: An Introduction, Princeton University Press, Princeton2003.3. I. Richards and H. Youn, Theory of Distributions and Non-technical Approach, Cambridge UniversityPress, Cambridge, 1990.References:1. Stein, E.M., Singular integrals and differentiability properties of functions, 1970.2. Sadosky, C., Interpolation of operators and singular integrals, 1979.3. Dym, H. and Mckean, H.P., Fourier series and integrals, 1972.4. Katznelson, Harmonic Analysis.