The Asymptotic Behaviour of Semigroups of Linear Operators: 88 (Operator Theory: Advances and Applications, 88) - Hardcover
Synopsis
Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO"(A)) = O"(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h~o, i. e. the infimum of all wE JR such that II exp(tA)II :::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A : A E O"(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t , u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo- nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A.
"synopsis" may belong to another edition of this title.
Synopsis
The focus of this text is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. Recent developments in the field are covered, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapping theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroups in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability.
"About this title" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for The Asymptotic Behaviour of Semigroups of Linear Operators:...
Stock Image
The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications, 88)
Seller: Lucky's Textbooks, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # ABLIING23Apr0316110058796
Stock Image
The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications, 88)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9783764354558_new
Buy New
£ 94.13
Shipping:
£ 11.98
From United Kingdom to U.S.A.
Quantity: Over 20 available
Seller Image
The Asymptotic Behaviour of Semigroups of Linear Operators
Published by
Springer, Basel, Birkhäuser Basel, Birkhäuser Jul 1996, 1996
ISBN 10: 3764354550
ISBN 13: 9783764354558
New
Hardcover
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO'(A)) = O'(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h~o, i. e. the infimum of all wE JR such that II exp(tA)II :::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A : A E O'(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t , u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A. 241 pp. Englisch. Seller Inventory # 9783764354558
Seller Image
The Asymptotic Behaviour of Semigroups of Linear Operators
Seller: moluna, Greven, Germany
Seller rating 4 out of 5 stars
Gebunden. Condition: New. Seller Inventory # 5279134
Stock Image
The Asymptotic Behaviour Of Semigroups O
Seller: Kennys Bookshop and Art Galleries Ltd., Galway, GY, Ireland
Seller rating 5 out of 5 stars
Condition: New. Presents an account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. This work focuses on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. Series: Operator Theory: Advances and Applications. Num Pages: 253 pages, biography. BIC Classification: PBKF; PBKJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 15. Weight in Grams: 542. . 1996. Hardback. . . . . Seller Inventory # V9783764354558
Stock Image
The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications, 88)
Seller: BennettBooksLtd, San Diego, NV, U.S.A.
Seller rating 5 out of 5 stars
hardcover. Condition: New. In shrink wrap. Looks like an interesting title! Seller Inventory # Q-3764354550
Seller Image
The Asymptotic Behaviour of Semigroups of Linear Operators
Print on DemandSeller: preigu, Osnabrück, Germany
Seller rating 5 out of 5 stars
Buch. Condition: Neu. The Asymptotic Behaviour of Semigroups of Linear Operators | Jan Van Neerven | Buch | xii | Englisch | 1996 | Birkhäuser Basel | EAN 9783764354558 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. Seller Inventory # 101647508
Seller Image
The Asymptotic Behaviour of Semigroups of Linear Operators
Published by
Birkhäuser Basel, Birkhäuser Basel Jul 1996, 1996
ISBN 10: 3764354550
ISBN 13: 9783764354558
New
Hardcover
Seller: buchversandmimpf2000, Emtmannsberg, BAYE, Germany
Seller rating 5 out of 5 stars
Buch. Condition: Neu. Neuware -Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO'(A)) = O'(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h~o, i. e. the infimum of all wE JR such that II exp(tA)II :::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A : A E O'(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t , u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 256 pp. Englisch. Seller Inventory # 9783764354558
Seller Image
The Asymptotic Behaviour of Semigroups of Linear Operators
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO'(A)) = O'(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h~o, i. e. the infimum of all wE JR such that II exp(tA)II :::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A : A E O'(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t , u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A. Seller Inventory # 9783764354558
Stock Image
The Asymptotic Behaviour of Semigroups of Linear Operators
Seller: Buchpark, Trebbin, Germany
Seller rating 5 out of 5 stars
Condition: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 624567/2