000 04156nam a22004575i 4500
001 978-3-540-48322-9
003 DE-He213
005 20190213151623.0
007 cr nn 008mamaa
008 121227s1994 gw | s |||| 0|eng d
020 _a9783540483229
_9978-3-540-48322-9
024 7 _a10.1007/BFb0073401
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _adeLaubenfels, Ralph.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aExistence Families, Functional Calculi and Evolution Equations
_h[electronic resource] /
_cby Ralph deLaubenfels.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1994.
300 _aXVI, 244 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1570
505 0 _aIntuition and elementary examples -- Existence families -- Regularized semigroups -- The solution space of an operator and automatic well-posedness -- Exponentially bounded (Banach) solution spaces -- Well-posedness on a larger space; Generalized solutions -- Entire vectors and entire existence families -- Reversibility of parabolic problems -- The cauchy problem for the Laplace equation -- Boundary values of holomorphic semigroups -- The Schrödinger equation -- Functional calculus for commuting generators of bounded strongly continuous groups -- Petrovsky correct matrices of generators of bounded strongly continuous groups -- Arbitrary matrices of generators of bounded strongly continuous groups -- More examples of regularized semigroups -- Existence and uniqueness families -- C-resolvents and Hille-Yosida type theorems -- Relationship to integrated semigroups -- Perturbations -- Type of an operator -- Holomorphic C-existence families -- Unbounded holomorphic functional calculus for operators with polynomially bounded resolvents -- Spectral conditions guaranteeing solutions of the abstract Cauchy problem -- Polynomials of generators -- Iterated abstract Cauchy problems -- Equipartition of energy -- Simultaneous solution space -- Exponentially bounded simultaneous solution space -- Simultaneous existence families -- Simultaneous existence families for matrices of operators -- Time dependent evolution equations.
520 _aThis book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662188910
776 0 8 _iPrinted edition:
_z9783540577034
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1570
856 4 0 _uhttps://doi.org/10.1007/BFb0073401
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11305
_d11305