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These notes are a record of a one semester course on Functional Analysis given by the author to second year Master of Statistics students at the Indian Statistical Institute, New Delhi. Students taking this course have a strong background in real analysis, linear algebra, measure theory and probability, and the course proceeds rapidly from the definition of a normed linear space to the spectral theorem for bounded selfadjoint operators in a Hilbert space. The ...
This book is a collection of expository articles by well-known mathematicians. Some of them introduce the reader to a major topic while others provide a glimpse into an active field of research. All articles are accessible to graduate students. The articles were invited in honour of K.R. Parthasarathy, a mathematician, teacher and expositor of renown. Some of the articles, by his coworkers, are related to his work on probability, quantum probability and group ...
This book provides a quick introduction to Fourier Series. The author begins by describing one of the problems actually studied by Fourier and how this leads to a differential equation to solve which Fourier introduced his famous series. The mathematical problems this leads to are then discussed rigorously. After that, applications of the theory to four different problems are given. A novel feature of the book is the inclusion of a detailed history of the ...
This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. The author introduces ...