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Topics in Operator Semigroups de Shmuel Kantorovitz

Topics in Operator Semigroups

Autor Shmuel Kantorovitz
en Limba Engleză Hardback – dec 2009

Destinată nivelului de masterat și cercetării avansate, Topics in Operator Semigroups reprezintă o sinteză riguroasă a teoriei semigrupurilor de operatori liniari, filtrată prin perspectiva originală a lui Shmuel Kantorovitz. Observăm că această ediție din 2010 nu își propune o acoperire enciclopedică, ci se concentrează pe intersecția fertilă dintre semigrupuri și teoria spectrală, în special în ceea ce privește reprezentarea integrală a familiilor de operatori. Această alegere tematică distinge volumul de tratatele clasice, fiind o expansiune a monografiei sale anterioare și o continuare naturală a rigoarei metodologice demonstrate în Introduction to Modern Analysis. Structura narativă a textului urmează o progresie logică de la teoria de bază către aplicații complexe. Descoperim capitole esențiale despre analiticitate, valori la limită și pre-semigrupuri, culminând cu secțiuni dedicate sistemelor de evoluție și similarității. Remarcăm o atenție deosebită acordată spațiului de semi-simplitate și spațiului Laplace-Stieltjes, elemente care subliniază orientarea spre cercetare a lucrării. Comparabil cu A Short Course on Operator Semigroups de Klaus-Jochen Engel în ceea ce privește rigoarea demonstrațiilor, volumul de față este însă mai specific orientat către cercetătorii care urmăresc conexiunile cu analiza armonică și reprezentările integrale. Spre deosebire de abordarea introductivă din Semigroups of Linear Operators de David Applebaum, Shmuel Kantorovitz presupune o maturitate matematică ridicată, oferind instrumente avansate pentru studiul operatorilor nesimetrici și al sistemelor de evoluție.

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Specificații

ISBN-13: 9780817649319
ISBN-10: 081764931X
Pagini: 266
Ilustrații: XIV, 266 p.
Dimensiuni: 164 x 240 x 28 mm
Greutate: 0.55 kg
Ediția:2010 edition
Editura: BIRKHAUSER BOSTON INC
Locul publicării:Boston, MA, United States

Public țintă

Research

De ce să citești această carte

Această monografie este esențială pentru cercetătorii și studenții de la masterat care doresc să aprofundeze legătura dintre teoria spectrală și semigrupurile de operatori. Dincolo de fundamentele teoretice, volumul oferă acces la direcții de cercetare specifice autorului, fiind un instrument de lucru prețios pentru cei specializați în analiză funcțională care caută o perspectivă modernă asupra reprezentărilor integrale.

Descriere scurtă

This book is based on lecture notes from a second-year graduate course, and is a greatly expanded version of our previous monograph [K8]. We expose some aspects of the theory of semigroups of linear operators, mostly (but not only) from the point of view of its meeting with that part of spectral theory which is concerned with the integral representation of families of operators. This approach and selection of topics di?erentiate this book from others in the general area, and re?ect the author’s own research directions. There is no attempt therefore to cover thoroughly the theory of semigroups of operators. This theory and its applications are extensively exposed in many books, from theclassicHille–Phillipsmonograph[HP]tothemostrecenttextbookofEngel and Nagel [EN2] (see [A], [BB], [Cl], [D3], [EN1], [EN2], [Fat], [G], [HP], [P], [Vr], and others), as well as in chapters in more general texts on Functional Analysis and the theory of linear operators (cf. [D5], [DS I–III], [Kat1], [RS], [Y], and many others).

Cuprins

General Theory.- Basic Theory.- The Semi-Simplicity Space for Groups.- Analyticity.- The Semigroup as a Function of its Generator.- Large Parameter.- Boundary Values.- Pre-Semigroups.- Integral Representations.- The Semi-Simplicity Space.- The Laplace#x2013;Stieltjes Space.- Families of Unbounded Symmetric Operators.- A Taste of Applications.- Analytic Families of Evolution Systems.- Similarity.

Recenzii

From the book reviews:
“This monograph is suitable for second-year graduate students, but it can be recommended also to any researcher interested in operator semigroups.” (László Kérchy, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)
“The present graduate level text expands the previous lecture notes from the same author, Semigroups of operators and spectral theory … . It begins with a succinct introduction to operator semigroups covering classical topics such as generators, the Hille-Yosida theorem, dissipative operators and the Lumer–Phillips theorem, the Trotter convergence theorem, exponential formulas, perturbation theory, Stone’s theorem, and analytic semigroups. … The text is also intended for second-year graduate students … . it will be a valuable source for researchers working in this area.” (G. Teschl, Monatshefte für Mathematik, Vol. 162 (4), April, 2011)
“This book is based on the author’s lecture notes … in which the more advanced parts concentrated on spectral representations. … There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. … The increased variety of topics covered will make the book more useful … . Other advantages are the inclusion of an index and some exercises, considerable extensions of the bibliography and the list of contents, and more attractive typesetting.”­­­ (C. J. K. Batty, Mathematical Reviews, Issue 2010 k)

Textul de pe ultima copertă

The theory of operator semigroups was essentially discovered in the early 1930s.  Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics such as Markov processes, the abstract Cauchy problem, evolution equations, and mathematical physics.
This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectral theory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications.
Topics include:
* The Hille–Yosida and Lumer–Phillips characterizations of semigroup generators
* The Trotter–Kato approximation theorem
* Kato’s unified treatment of the exponential formula and the Trotter product formula
* The Hille–Phillips perturbation theorem, and Stone’s representation of unitary semigroups
*  Generalizations of spectral theory’s connection to operator semigroups
* A natural generalization of Stone’s spectral integral representation to a Banach space setting
With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operator semigroups.

Caracteristici

Concerned with the interplay between the theory of operator semigroups and spectral theory The basics on operator semigroups are concisely covered in this self-contained text Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato’s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone’s representation of unitary semigroups Part II explores generalizations of spectral theory’s connection to operator semigroups Suitable for a graduate seminar on operator semigroups or for self study Includes supplementary material: sn.pub/extras