Bøger af Rainer Nagel

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.

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.

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.

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.