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1995 | 114 | 3 | 237-259
Tytuł artykułu

Automatic extensions of functional calculi

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a Banach algebra ℱ of complex-valued functions and a closed, linear (possibly unbounded) densely defined operator A, on a Banach space, with an ℱ functional calculus we present two ways of extending this functional calculus to a much larger class of functions with little or no growth conditions. We apply this to spectral operators of scalar type, generators of bounded strongly continuous groups and operators whose resolvent set contains a half-line. For f in this larger class, one construction measures how far f(A) is from generating a strongly continuous semigroup, while the other construction measures how far f(A) is from being bounded. We apply our constructions to evolution equations.
Słowa kluczowe
Czasopismo
Rocznik
Tom
114
Numer
3
Strony
237-259
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-10-25
poprawiono
1995-01-03
Twórcy
Bibliografia
  • [1] M. Balabane, H. Emamirad and M. Jazar, Spectral distributions and generalization of Stone's theorem to the Banach space, Acta Appl. Math. 31 (1993), 275-295.
  • [2] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248.
  • [3] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
  • [4] R. deLaubenfels, Unbounded holomorphic functional calculus for operators with polynomially bounded resolvents, J. Funct. Anal. 114 (1993), 348-394.
  • [5] R. deLaubenfels, Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Math. 1570, Springer, 1994.
  • [6] H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, 1978.
  • [7] N. Dunford and J. T. Schwartz, Linear Operators, Part III, Interscience, New York, 1971.
  • [8] E. Marschall, Functional calculi for closed linear operators in Banach spaces, Manuscripta Math. 35 (1981), 277-310.
  • [9] L. E. Payne, Improperly Posed Problems in Partial Differential Equations, SIAM, Philadelphia, Pa., 1975.
  • [10] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv114i3p237bwm
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