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- catalog abstract "This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.".
- catalog contributor b11038598.
- catalog contributor b11038599.
- catalog created "1998.".
- catalog date "1998".
- catalog date "1998.".
- catalog dateCopyrighted "1998.".
- catalog description "Includes bibliographical references and index.".
- catalog description "Laplace transforms and operator families in locally convex spaces -- Wellposedness and solvability -- Generalized wellposedness -- Analyticity and parabolicity -- Exponential growth bound and exponential stability -- Differentiability and norm continuity -- Almost periodicity -- Appendices: A1 Fractional powers of non-negative operators -- A2 Strongly continuous semigroups and cosine functions -- Bibliography -- Index -- Symbols.".
- catalog description "This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis.".
- catalog extent "xii, 300 p. ;".
- catalog identifier "3540652388 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1701.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1701".
- catalog issued "1998".
- catalog issued "1998.".
- catalog language "eng".
- catalog publisher "New York : Springer Verlag,".
- catalog subject "510 s 515/.35 21".
- catalog subject "Banach spaces.".
- catalog subject "Cauchy problem.".
- catalog subject "Differential equations.".
- catalog subject "Hilbert space.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1701 QA371".
- catalog tableOfContents "Laplace transforms and operator families in locally convex spaces -- Wellposedness and solvability -- Generalized wellposedness -- Analyticity and parabolicity -- Exponential growth bound and exponential stability -- Differentiability and norm continuity -- Almost periodicity -- Appendices: A1 Fractional powers of non-negative operators -- A2 Strongly continuous semigroups and cosine functions -- Bibliography -- Index -- Symbols.".
- catalog title "The Cauchy problem for higher order abstract differential equations / Ti-Jun Xiao, Jin Liang.".
- catalog type "text".