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001 978-3-031-56720-9
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008 240611s2024 sz | s |||| 0|eng d
020 _a9783031567209
_9978-3-031-56720-9
024 7 _a10.1007/978-3-031-56720-9
_2doi
050 4 _aQA329-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
100 1 _aZagrebnov, Valentin A.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978557
245 1 0 _aTrotter-Kato Product Formulæ
_h[electronic resource] /
_cby Valentin A. Zagrebnov, Hagen Neidhardt, Takashi Ichinose.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXX, 873 p. 7 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aOperator Theory: Advances and Applications,
_x2296-4878 ;
_v296
505 0 _a- 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.
520 _aThe 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.
650 0 _aOperator theory.
650 0 _aDifferential equations.
650 1 4 _aOperator Theory.
650 2 4 _aDifferential Equations.
700 1 _aNeidhardt, Hagen.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978558
700 1 _aIchinose, Takashi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978559
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031567193
776 0 8 _iPrinted edition:
_z9783031567216
776 0 8 _iPrinted edition:
_z9783031567223
830 0 _aOperator Theory: Advances and Applications,
_x2296-4878 ;
_v296
_974617
856 4 0 _uhttps://doi.org/10.1007/978-3-031-56720-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c60657
_d60657