000 03878nam a22004695i 4500
001 978-3-0348-0087-7
003 DE-He213
005 20140220083739.0
007 cr nn 008mamaa
008 110404s2011 sz | s |||| 0|eng d
020 _a9783034800877
_9978-3-0348-0087-7
024 7 _a10.1007/978-3-0348-0087-7
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aArendt, Wolfgang.
_eauthor.
245 1 0 _aVector-valued Laplace Transforms and Cauchy Problems
_h[electronic resource] :
_bSecond Edition /
_cby Wolfgang Arendt, Charles J.K. Batty, Matthias Hieber, Frank Neubrander.
264 1 _aBasel :
_bSpringer Basel,
_c2011.
300 _aXII, 540 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMonographs in Mathematics ;
_v96
505 0 _aPreface to the First Edition -- Preface to the Second Edition -- I Laplace Transforms and Well-Posedness of Cauchy Problems -- 1 The Laplace Integral -- 2 The Laplace Transform -- 3 Cauchy Problems -- II Tauberian Theorems and Cauchy Problems -- 4 Asymptotics of Laplace Transforms -- 5 Asymptotics of Solutions of Cauchy Problems -- III Applications and Examples -- 6 The Heat Equation -- 7 The Wave Equation -- 8 Translation Invariant Operators on Lp(Rn) -- A Vector-valued Holomorphic Functions -- B Closed Operators -- C Ordered Banach Spaces -- D Banach Spaces which Contain c0 -- E Distributions and Fourier Multipliers -- Bibliography -- Notation -- Index.
520 _aThis monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The authors have succeeded admirably in bringing together a wealth of recent material, much of which appears in book form for the first time. This authoritative work is likely to become a standard reference on both the Laplace transform and its applications to the abstract Cauchy problem. … The book is an excellent textbook as well. Proofs are always transparent and complete, and many topics that could have been considered as background material are covered as well. All this makes the text very accessible and self-contained. Applications to concrete differential operators are given throughout the text. Each chapter ends with historical and bibliographical comments. … In summary, this book will be of interest to a wide audience of (functional) analysts and it should have a place in every mathematics library. Warmly recommended! Jan van Neerven, Nieuw Archief voor Wiskunde, No. 3, 2003
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
700 1 _aBatty, Charles J.K.
_eauthor.
700 1 _aHieber, Matthias.
_eauthor.
700 1 _aNeubrander, Frank.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034800860
830 0 _aMonographs in Mathematics ;
_v96
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0087-7
912 _aZDB-2-SMA
999 _c106591
_d106591