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1997 | 38 | 1 | 325-338
Tytuł artykułu

Empathy theory and the Laplace transform

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.
Słowa kluczowe
Rocznik
Tom
38
Numer
1
Strony
325-338
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
  • Faculty of Science, University of Pretoria, Pretoria 0002, South Africa
Bibliografia
  • [Are87] W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352.
  • [AF93] W. Arendt and A. Favini, Integrated solutions to implicit differential equations, Rend. Sem. Mat. Univ. Pol. Torino 51 (1993), 315-329.
  • [CaSh76] R. W. Carroll and R. Showalter, Singular and Degenerate Cauchy Problems, Academic Press, New York, 1976.
  • [CS94] W. L. Conradie and N. Sauer, Empathy, C-semigroups and integrated semigroups, in: Evolution Equations, Proc. Conf. Baton Rouge 1993, G. Ferreyra, G. R. Goldstein and F. Neubrander (eds.), Lecture Notes in Pure and Appl. Math. 168, Marcel Dekker, New York, 1995, 123-132.
  • [daP66] G. da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-246.
  • [DP87] E. B. Davies and M. M. Pang, The Cauchy problem and a generalization of the Hille-Yosida theorem, Proc. London Math. Soc. 55 (1987), 181-208.
  • [DeL91] R. deLaubenfels, Existence and uniqueness families, for the abstract Cauchy problem, J. London Math. Soc. 44 (1991), 310-338.
  • [DeL94] R. deLaubenfels, Existence Families, Functional Calculus and Evolution Equations, Lecture Notes in Math. 1570, Springer, Berlin, 1994.
  • [DU77] J. Diestel and J. J. Uhl Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., Providence, R.I., 1977.
  • [Fav79] A. Favini, Laplace transform method for a class of degenerate evolution equations, Rend. Mat. 3-4 (1979), 511-536.
  • [Fri58] K. O. Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 333-418.
  • [HP57] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31, 1957.
  • [Miy51] I. Miyadera, One parameter semi-groups of operators, J. Math. Tokyo 8 (1951), 23-26.
  • [Sau82] N. Sauer, Linear evolution equations in two Banach spaces, Proc. Roy. Soc. Edinburgh 91A (1982), 387-303.
  • [Sau95] N. Sauer, Implicit evolution equations and empathy theory, in: Recent Developments in Evolution Equations, Pitman Res. Notes in Math. Ser. 324, A. C. McBride and G. F. Roach (eds.), Longman, Harlow, 1995, 32-39.
  • [SS87] N. Sauer and J. E. Singleton, Evolution operators related to semigroups of class (A), Semigroup Forum 35 (1987), 317-335.
  • [SS89] N. Sauer and J. E. Singleton, Evolution operators in empathy with a semigroup, ibid. 39 (1989), 85-94.
  • [Wid46] D. V. Widder, The Laplace Transform, Princeton Univ. Press, 2nd printing, 1946.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv38i1p325bwm
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