ENGLISH

Trotter-Kato Product Formulæ

By Valentin A. Zagrebnov , Hagen Neidhardt , Takashi Ichinose

Book information

Publisher
Birkhäuser
Year
2024
ISBN
9783031567209
DOI
10.1007/978-3-031-56720-9
ISSN
2296-4878
Language
english
Format
DJVU
Filesize
8 MB (8740348 bytes)
Series
Operator Theory: Advances and Applications 296
Edition
1
Pages
873\879
DPI
400
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-06-12 10:36:56
Operator SemigroupsTrotter-Kato Product Formulae

Description

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 operat

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