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The main aim of this book is to introduce the reader to the concept of comparison algebra, defined as a type of C*-algebra of singular integral operators. The first part of the book develops the necessary elements of the spectral theory of differential operators as well as the basic properties of elliptic second order differential operators. The author then introduces comparison algebras and describes their theory in L2-spaces and L2-Soboler spaces, and in particular their importance in solving functional analytic problems involving differential operators. The book is based on lectures given in Sweden and the USA.

Differential operators. --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Operators, Differential --- Differential equations

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The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supercyclicity, the authors assemble the wide body of theory that has received much attention over the last fifteen years and present it for the first time in book form. Selected topics include various kinds of 'existence theorems', the role of connectedness in hypercyclicity, linear dynamics and ergodic theory, frequently hypercyclic and chaotic operators, hypercyclic subspaces, the angle criterion, universality of the Riemann zeta function, and an introduction to operators without non-trivial invariant subspaces. Many original results are included, along with important simplifications of proofs from the existing research literature, making this an invaluable guide for students of the subject. This book will be useful for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.

Linear operators. --- Mathematics. --- Math --- Science --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory

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Hilbert space. --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Banach spaces --- Hyperspace --- Inner product spaces

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Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.

Linear operators. --- Linear systems. --- Systems, Linear --- Differential equations, Linear --- System theory --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory

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Linear operators. --- 517.98 --- Linear operators --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Functional analysis and operator theory --- 517.98 Functional analysis and operator theory