Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

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The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure a nd applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.Format: HardcoverNo of Pages: 252Imprint: World ScientificPublication date: 20210118 Show more