Rainer Nagel

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include:• an intuitive introduction to ergodic theory• an introduction to the basic notions, constructions, and standard examples of topological dynamical systems• Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem• measure-preserving dynamical systems• von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem• strongly and weakly mixing systems• an examination of notions of isomorphism for measure-preserving systems• Markov operators, and the related concept of a factor of a measure preserving system• compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition• an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy)Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include:• an intuitive introduction to ergodic theory• an introduction to the basic notions, constructions, and standard examples of topological dynamical systems• Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem• measure-preserving dynamical systems• von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem• strongly and weakly mixing systems• an examination of notions of isomorphism for measure-preserving systems• Markov operators, and the related concept of a factor of a measure preserving system• compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition• an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy)Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.

ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented this beautiful theory, together with many applications, and tried to show the progress made since the pub- cation in 1957 of the now classical monograph [HP57] by E. Hille and R. Phillips. However, the wealth of results exhibited in our Graduate Text seems to have discouraged some of the potentially interested readers. With the present text we o?er a streamlined version that strictly sticks to the essentials. We have skipped certain parts, avoided the use of sophisticated arguments,and,occasionally,weakenedtheformulationofresultsandm- i?ed the proofs. However, to a large extent this book consists of excerpts taken from our Graduate Text, with some new material on positive se- groups added in Chapter VI. We hope that the present text will help students take their ?rst step into this interesting and lively research ?eld. On the other side, it should provide useful tools for the working mathematician. Acknowledgments This book is dedicated to our students. Without them we would not be able to do and to enjoy mathematics. Many of them read previous versions when it served as the text of our Seventh Internet Seminar 2003/04. Here Genni Fragnelli, Marc Preunkert and Mark C. Veraar were among the most active readers. Particular thanks go to Tanja Eisner, Vera Keicher, Agnes Radl for proposing considerable improvements in the ?nal version.

ThetheoryofstronglycontinuoussemigroupsoflinearoperatorsonBanach spaces, operator semigroups for short, has become an indispensable tool in a great number of areas of modern mathematical analysis. In our Springer Graduate Text [EN00] we presented this beautiful theory, together with many applications, and tried to show the progress made since the pub- cation in 1957 of the now classical monograph [HP57] by E. Hille and R. Phillips. However, the wealth of results exhibited in our Graduate Text seems to have discouraged some of the potentially interested readers. With the present text we o?er a streamlined version that strictly sticks to the essentials. We have skipped certain parts, avoided the use of sophisticated arguments,and,occasionally,weakenedtheformulationofresultsandm- i?ed the proofs. However, to a large extent this book consists of excerpts taken from our Graduate Text, with some new material on positive se- groups added in Chapter VI. We hope that the present text will help students take their ?rst step into this interesting and lively research ?eld. On the other side, it should provide useful tools for the working mathematician. Acknowledgments This book is dedicated to our students. Without them we would not be able to do and to enjoy mathematics. Many of them read previous versions when it served as the text of our Seventh Internet Seminar 2003/04. Here Genni Fragnelli, Marc Preunkert and Mark C. Veraar were among the most active readers. Particular thanks go to Tanja Eisner, Vera Keicher, Agnes Radl for proposing considerable improvements in the ?nal version.

This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.

Besonderheiten herauskristallisieren. Die Arbeit stellt einen Beitrag zur angewandten Fachsprachen- sowie zur englischen Wortbildungsforschung dar. Die untersuchten Texte entstammen einer seit 1973 belegten Art der Gesellschaftsspiele, dem Fantasy-Rollenspiel, das in den USA auf Grundlage der aus den Sozialwissenschaften bekannten Rollenspiele entwickelt wurde. Fantasy-Rollenspiele werden in ein allgemeines Fachsprachen-Modell eingebunden und nach modernen Wortbildungstheorien untersucht, wobei sich einige im "Standard English" nicht anzutreffende Besonderheiten herauskristallisieren.