Spectral Theory of Dynamical Systems

Mahendra Nadkarni is Emeritus Professor of mathematics at the University of Mumbai, India. He earned his M.Sc. degree in Mathematics from the University of Mumbai in 1960 and Ph.D. in applied mathematics from Brown University in1965. His research and pedagogic interests are in the areas of ergodic theory, harmonic analysis and probability theory in which he has scholarly publications including a book titled Basic Ergodic Theory. He is Fellow of the Indian National Science Academy, New Delhi, and, the Indian Academy of Sciences, Bengaluru. He has taught at the Indian Statistical Institute, Kolkata; the University of Minnesota, Minneapolis; Chennai Mathematical Institute, Chennai; the Indian Institute of Technology Indore; the Indian Institute of Technology Kanpur; Center of Excellence in Basic Sciences, Mumbai; and had visiting appointments at McGill University, Universities of York and Toronto in Canada. 

The Hahn-Hellinger Theorem.- The Spectral Theorem for Unitary Operators.- Symmetry and Denseness of the Spectrum.- Multiplicity and Rank.- The Skew Product.- A Theorem of Helson and Parry.- Probability Measures on the Circle Group.- Baire Category Theorems of Ergodic Theory.- Translations of Measures on the Circle.- B. Host's Theorem.- L∞ Eigenvalues of Non-Singular Automorphisms.- Generalities on Systems of Imprimitivity.- Dual Systems of Imprimitivity.- Saturated Subgroups of the Circle Group.- Riesz Products As Spectral Measures.- Additional Topics.- Calculus of Generalized Riesz Products.