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One-Parameter Semigroups for Linear Evolution Equations de Klaus-Jochen Engel

One-Parameter Semigroups for Linear Evolution Equations: Graduate Texts in Mathematics, cartea 194

Autor Klaus-Jochen Engel, Rainer Nagel
en Limba Engleză Hardback – 29 oct 1999

Notăm cu interes acest manual de referință publicat în seria Graduate Texts in Mathematics, care s-a impus ca o resursă fundamentală pentru studiul teoriei semigrupurilor de operatori liniari. One-Parameter Semigroups for Linear Evolution Equations reprezintă o sinteză riguroasă a operatorilor liniari continuu-stabili, fiind concepută pentru a servi atât ca suport de curs pentru nivelul de masterat și doctorat, cât și ca monografie de cercetare.

Remarcăm structura logică a volumului, care pornește de la fundamentele sistemelor dinamice liniare și generatori, avansând spre subiecte complexe precum teoria perturbațiilor și a aproximării. Spre deosebire de alte lucrări pur abstracte, Klaus-Jochen Engel și Rainer Nagel alocă spații generoase aplicațiilor practice, integrând teoria semigrupurilor în contextul ecuațiilor cu întârziere, al teoriei controlului și al operatorilor diferențiali. Cartea extinde cadrul propus de A Short Course on Operator Semigroups (scrisă de același Klaus-Jochen Engel) prin oferirea unui aparat demonstrativ mult mai detaliat și a unui context istoric bogat, care urmărește evoluția conceptului de la funcția exponențială la operatorii moderni.

În comparație cu textul clasic al lui Amnon Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, lucrarea de față aduce la zi rezultatele din a doua jumătate a secolului XX, punând un accent deosebit pe asimptotica semigrupurilor și pe teoria spectrală. Finalul cărții, care include o scurtă istorie a funcției exponențiale, oferă cititorului o perspectivă filosofică rară în literatura matematică tehnică, facilitând înțelegerea motivațiilor din spatele formalismului abstract.

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Specificații

ISBN-13: 9780387984636
ISBN-10: 0387984631
Pagini: 616
Ilustrații: XXI, 589 p.
Dimensiuni: 160 x 241 x 38 mm
Greutate: 1.08 kg
Ediția:2000
Editura: Springer
Colecția Graduate Texts in Mathematics
Seria Graduate Texts in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Research

De ce să citești această carte

Recomandăm acest volum cercetătorilor și studenților avansați în matematică care doresc o stăpânire profundă a analizei funcționale aplicate. Cititorul câștigă acces la un set complet de instrumente pentru rezolvarea ecuațiilor de evoluție, beneficiind de o prezentare care îmbină rigoarea teoremei Hille-Yosida cu aplicații concrete în fizică și inginerie. Este, fără îndoială, succesorul modern al monografiilor clasice din domeniu.

Cuprins

Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.- Semigroups Everywhere.- A Brief History of the Exponential Function.

Recenzii

From the reviews:
"This book is a real asset for people who work in the field of operator semigroups, or want to. It is a beauty, not only because it contains so much information, but also because the authors have done everything conceivable to put the whole subject in the right historical and contemporary context." (J. van Casteren, Nieuw Archief voor Wiskunde, Vol. 5/6 (4), 2005)
"This is an excellent introduction to semigroups of operators and applications. … The book can be recommended primarily to graduate students, but it is also of interest to researchers." (Tibor Krisztin, Acta Scientiarum Mathematicarum, Vol. 69, 2003)
"This book is a continuation of a series of monographs on one-parameter semigroups … . The book is well written. … It contains a sufficient number of instructive examples in every chapter. … Moreover, a lot of exercises are given which may help to understand the abstract theory. Altogether the book can also be used as a good basis for a series of lectures on that topic." (M. Demuth, Jahresberichte der Deutschen Mathematiker Vereinigung, Vol. 104 (1), 2002)
"The present volume can be considered an up-to-date exposition of the theory and applications of linear semigroup theory … . A detailed history of the exponential function and its connection with semigroup theory gives interesting information … . A useful appendix is added to help the reader … . In conclusion, by virtue of its clearness of style and ease of consultation, this book can be recommended to the beginners as well as to the experts in semigroup theory … ." (Gabriella Di Blasio, Semigroup Forum, Vol. 63 (2), 2001)
"In this book the authors give an excellent presentation of the theory of semigroups … . The reader can use the text as an introduction … . At the same time, this book contains many new and very recent results of the theory and its application, thus it is also of great value for experts. … Notes atthe end of each chapter contain many hints to additional material. Each section ends with a collection of exercises. … The book turned out very well." (Karl-Heinz Förster, Zentralblatt MATH, Vol. 952, 2001)
"The book offers an introduction to strongly continuous one-parameter semigroups in Banach spaces. … The book is very well written. Besides the basic text it contains many illustrating examples, exercises and notes. It will certainly be very useful for advanced students and for those mathematicians who want to be acquainted with the most recent results of the field. … also those who are interested in functional analytic ideas and methods will enjoy reading it." (H. Langer, Internationale Mathematische Nachrichten, Issue 185, 2000)
"This book provides a comprehensive and up-to-date introduction to, and exposition of, the theory of strongly continuous one-parameter semigroups of linear operators and of its applications … . The book is clearly written, well organized, provides much information and numerous examples … . Therefore, I can highly recommend this book both to students with a background in basic functional analysis as an introduction into this field, as well as to researchers as a modern and comprehensive exposition of the theory and its applications." (R. Bürger, Monatshefte für Mathematik, Vol. 131 (2), 2000)
"This book is a broad introduction to the theory of C0-semigroups. … The steady pace of the text and the very high quality of the exposition make the material in this book easily accessible … . the book’s greatest impact is likely to be through tempting graduate students to learn about semigroups of operators … . the book should also be of interest to experienced researchers. Most specialists in semigroup theory and applications will be glad to have it … ." (C. J. K. Batty, Mathematical Reviews, Issue 2000 i)

Descriere

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.