UID:
almahu_9949773125702882
Umfang:
XX, 873 p. 7 illus., 1 illus. in color.
,
online resource.
Ausgabe:
1st ed. 2024.
ISBN:
9783031567209
Serie:
Operator Theory: Advances and Applications, 296
Inhalt:
The book captures a fascinating snapshot of the current state of results about the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces. It also includes results on the operator-norm convergent product formulæ for solution operators of the non-autonomous Cauchy problems as well as similar results on the unitary and Zeno product formulæ. After the Sophus Lie product formula for matrices was established in 1875, it was generalised to Hilbert and Banach spaces for convergence in the strong operator topology by H. Trotter (1959) and then in an extended form by T. Kato (1978). In 1993 Dzh. L. Rogava discovered that convergence of the Trotter product formula takes place in the operator-norm topology. The latter is the main subject of this book, which is dedicated essentially to the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces, but also to related results on the time-dependent, unitary and Zeno product formulæ. The book yields a detailed up-to-date introduction into the subject that will appeal to any reader with a basic knowledge of functional analysis and operator theory. It also provides references to the rich literature and historical remarks.
Anmerkung:
- Part I Preliminaries -- Semigroups and their generators -- Linear Evolution Equations -- Quasi-sectorial contractions and operator-norm convergence -- Part II: Trotter-Kato product formulæ for self-adjoint semigroups -- Product approximations of self-adjoint semigroups -- Trotter-Kato product formulæ: strong operator topology -- Trotter-Kato product formulæ: operator-norm topology -- Trotter-Kato product formulae: operator-norm topology and error bounds -- Part III: Trotter-Kato product formulæ for non-self-adjoint semigroups -- Operator-norm approximation theory `a la Cherno -- Product formulæ for non-self-adjoint semigroups -- Operator-norm Trotter product formula on Banach spaces -- Part IV: Time-dependent product formulæ. - Time-dependent product formulæ: Banach space -- Time-dependent product formulæ: Hilbert space -- Part V: Unitary and Zeno product formulæ -- Unitary product formulæ. - Zeno product formulæ.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783031567193
Weitere Ausg.:
Printed edition: ISBN 9783031567216
Weitere Ausg.:
Printed edition: ISBN 9783031567223
Sprache:
Englisch
Fachgebiete:
Mathematik
Schlagwort(e):
Llibres electrònics
DOI:
10.1007/978-3-031-56720-9
URL:
https://doi.org/10.1007/978-3-031-56720-9
URL:
Volltext
(URL des Erstveröffentlichers)
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