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1999 | 137 | 2 | 161-167
Tytuł artykułu

$H^∞$ functional calculus in real interpolation spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let A be a linear closed densely defined operator in a complex Banach space X. If A is of type ω (i.e. the spectrum of A is contained in a sector of angle 2ω, symmetric around the real positive axis, and $∥λ(λ I - A)^{-1}∥$ is bounded outside every larger sector) and has a bounded inverse, then A has a bounded $H^∞$ functional calculus in the real interpolation spaces between X and the domain of the operator itself.
Słowa kluczowe
Czasopismo
Rocznik
Tom
137
Numer
2
Strony
161-167
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-07-10
poprawiono
1999-07-30
Twórcy
  • Dipartimento di Matematica, Università di Bologna, Piazza di Porta, S. Donato 5, 40127 Bologna, Italy , dore@dm.unibo.it
Bibliografia
  • [1] K. N. Boyadzhiev and R. J. deLaubenfels, $H^∞$ functional calculus for perturbations of generators of holomorphic semigroups, Houston J. Math. 17 (1991), 131-147.
  • [2] K. N. Boyadzhiev and R. J. deLaubenfels, Semigroups and resolvents of bounded variation, imaginary powers and $H^∞$ functional calculus, Semigroup Forum 45 (1992), 372-384.
  • [3] M. Cowling, I. Doust, A. McIntosh and A. Yagi, Banach space operators with a bounded $H^∞$ functional calculus, J. Austral. Math. Soc. Ser. A 60 (1996), 51-89.
  • [4] G. Dore and A. Venni, Some results about complex powers of closed operators, J. Math. Anal. Appl. 149 (1990), 124-136.
  • [5] R. deLaubenfels, A holomorphic functional calculus for unbounded operators, Houston J. Math. 13 (1987), 545-548.
  • [6] R. deLaubenfels, Unbounded holomorphic functional calculus and abstract Cauchy problems for operators with polynomially bounded resolvents, J. Funct. Anal. 114 (1993), 348-394.
  • [7] A. McIntosh, Operators which have an $H_∞$ functional calculus, in: Miniconference on Operator Theory and Partial Differential Equations (Macquarie University, Ryde, N.S.W., September 8-10, 1986), B. Jefferies, A. McIntosh and W. Ricker (eds.), Proc. Centre Math. Anal. Austral. Nat. Univ. 14, Austral. Nat. Univ., Canberra, 1986, 210-231.
  • [8] A. McIntosh and A. Yagi, Operators of type ω without a bounded $H_∞$ functional calculus, in: Miniconference on Operators in Analysis (Macquarie University, Sydney, N.S.W., September 25-27, 1989), I. Doust, B. Jefferies, C. Li and A. McIntosh (eds.), Proc. Centre Math. Anal. Austral. Nat. Univ. 24, Austral. Nat. Univ., Canberra, 1989, 159-172.
  • [9] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv137i2p161bwm
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