04067nam a22004935i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001700188072002300205072001600228100009100244245012100335250001800456264007300474300006200547336002600609337002600635338003600661347002400697490006600721505094600787520123601733650002102969650002802990650002103018650002803039700008603067700008703153710003403240773002603274776003603300776003603336776003603372830007303408856004603481912001403527912001503541999001703556978-3-031-56720-9DE-He21320251030112307.0cr nn 008mamaa240611s2024    sz |    s    |||| 0|eng d  a97830315672099978-3-031-56720-97 a10.1007/978-3-031-56720-92doi 4aQA329-329.9 7aPBKF2bicssc 7aMAT0370002bisacsh 7aPBKF2thema1 aZagrebnov, Valentin A.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97855710aTrotter-Kato Product Formulæh[electronic resource] /cby Valentin A. Zagrebnov, Hagen Neidhardt, Takashi Ichinose.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXX, 873 p. 7 illus., 1 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aOperator Theory: Advances and Applications,x2296-4878 ;v2960 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.  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. 0aOperator theory. 0aDifferential equations.14aOperator Theory.24aDifferential Equations.1 aNeidhardt, Hagen.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9785581 aIchinose, Takashi.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9785592 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303156719308iPrinted edition:z978303156721608iPrinted edition:z9783031567223 0aOperator Theory: Advances and Applications,x2296-4878 ;v29697461740uhttps://doi.org/10.1007/978-3-031-56720-9  aZDB-2-SMA  aZDB-2-SXMS  c60657d60657