Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.

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-Sarkoezy) 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.

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. It contains the fundamental results of the theory such as the Hille-Yoshida generation theorem, the bounded perturbation theorem, and the Trotter-Kato approximation theorem. It also treats the spectral theory of semigroups and its consequences for the qualitative behavior. The book is intended for students and researchers who want to become acquainted with the concept of semigroups in order to work with it in fields like partial and functional differential equations. Exercises are provided at the end of the chapters.

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L DEGREESp-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

This book gives an up-to-date account of the theory of strongly continuous one-parameter semigroups of linear operators. It includes a systematic discussion of the spectral theory and the long-term behavior of such semigroups. A special feature of the text is an unusually wide range of applications, e.g., to ordinary and partial differential operators, delay and Volterra equations and to control theory, and an emphasis on philosophical motivation and the historical background. The book is written for students, but should also be of value for researchers interested in this field.

Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.

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-Sarkoezy) 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

J.R.R. Tolkien's giving of names has garnered considerable attention in the linguistic analysis of Tolkien's works. Usually, however, the focus has been on singling out particular names of important individuals and places. Thorough analyses of names (place-names or personal ones) are usually reserved for Elvish names only. Thus, this book centres on the place-names as found in the Shire as well as Breeland. All those names that are referenced on Tolkien's map of the Shire, plus those few that are not found on the map but mentioned in the text, as well as four from The Adventures of Tom Bombadil, are analysed as to their possible "etymologies" against the theoretical backdrop of real-world English place-name research. Tolkien's "own" (in-world) etymologies, insofar as they differ from the real-world ones, are also taken into consideration. Finally, all extant German translations (Scherf and Krege for The Hobbit, Carroux and Krege for The Lord of the Rings) of these names are given and, where necessary, compared. Other media (the films and the Hobbit graphic novel, in particular) are also covered.

The relationship of philosophy with Kafka's oeuvre is complex. It has been argued that Kafka's novels and stories defy philosophic extrapolation; conversely, it has also been suggested that precisely the tendency of Kafka's writings to elude discursive solution is itself a philosophical tendency, one that is somehow contributing to a wiser relationship of human beings with language. These matters are the focus of the proposed volume on Philosophy and Kafka. The proposed collection brings together essays that interrogate the relationship of philosophy and Kafka, and offer new and original interpretations. The volume obviously cannot claim completeness, but it partially does justice to the multiplicity of philosophical issues and philosophical interpretations at stake. This variety informs the composition of the volume itself. A number of essays focus on specific philosophical commentaries on Kafka's work, from Adorno's to Agamben's, from Arendt's to Benjamin's, from Deleuze and Guattari's to Derrida's. A number of essays consider the possible relevance of certain philosophical outlooks for examining Kafka's writings: here Kafka's name goes alongside those of Socrates, Kant, Kierkegaard, Nietzsche, Wittgenstein, Buber, Heidegger, Blanchot, and Levinas. Finally, a number of essays consider Kafka's writings in terms of a specific philosophical theme, such as communication and subjectivity, language and meaning, knowledge and truth, the human/animal divide, justice, and freedom. In all contributions to the volume, such themes, motifs, and interpretations arise. To varying degrees, all essays are concerned with the relationship of literature and philosophy, and thus with the philosophical significance of Kafka's writings.

The relationship of philosophy with Kafka's oeuvre is complex. It has been argued that Kafka's novels and stories defy philosophic extrapolation; conversely, it has also been suggested that precisely the tendency of Kafka's writings to elude discursive solution is itself a philosophical tendency, one that is somehow contributing to a wiser relationship of human beings with language. These matters are the focus of the proposed volume on Philosophy and Kafka. The proposed collection brings together essays that interrogate the relationship of philosophy and Kafka, and offer new and original interpretations. The volume obviously cannot claim completeness, but it partially does justice to the multiplicity of philosophical issues and philosophical interpretations at stake. This variety informs the composition of the volume itself. A number of essays focus on specific philosophical commentaries on Kafka's work, from Adorno's to Agamben's, from Arendt's to Benjamin's, from Deleuze and Guattari's to Derrida's. A number of essays consider the possible relevance of certain philosophical outlooks for examining Kafka's writings: here Kafka's name goes alongside those of Socrates, Kant, Kierkegaard, Nietzsche, Wittgenstein, Buber, Heidegger, Blanchot, and Levinas. Finally, a number of essays consider Kafka's writings in terms of a specific philosophical theme, such as communication and subjectivity, language and meaning, knowledge and truth, the human/animal divide, justice, and freedom. In all contributions to the volume, such themes, motifs, and interpretations arise. To varying degrees, all essays are concerned with the relationship of literature and philosophy, and thus with the philosophical significance of Kafka's writings.