04283nam a22005415i 4500 978-3-031-56720-9 DE-He213 20251030112307.0 cr nn 008mamaa 240611s2024 sz | s |||| 0|eng d 9783031567209 978-3-031-56720-9 10.1007/978-3-031-56720-9 doi QA329-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Zagrebnov, Valentin A. author. aut http://id.loc.gov/vocabulary/relators/aut 78557 Trotter-Kato Product Formulæ [electronic resource] / by Valentin A. Zagrebnov, Hagen Neidhardt, Takashi Ichinose. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XX, 873 p. 7 illus., 1 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Operator Theory: Advances and Applications, 2296-4878 ; 296 - 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. 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. Operator theory. Differential equations. Operator Theory. Differential Equations. Neidhardt, Hagen. author. aut http://id.loc.gov/vocabulary/relators/aut 78558 Ichinose, Takashi. author. aut http://id.loc.gov/vocabulary/relators/aut 78559 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031567193 Printed edition: 9783031567216 Printed edition: 9783031567223 Operator Theory: Advances and Applications, 2296-4878 ; 296 74617 https://doi.org/10.1007/978-3-031-56720-9 ZDB-2-SMA ZDB-2-SXMS 60657 60657