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On quasi-analytic vectors for dissipative operators


Author: Minoru Hasegawa
Journal: Proc. Amer. Math. Soc. 29 (1971), 81-84
MSC: Primary 47.50
DOI: https://doi.org/10.1090/S0002-9939-1971-0275224-9
MathSciNet review: 0275224
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Abstract: In this note we shall prove that a closed dissipative operator A with dense domain in a hilbert space H generates a contraction semigroup if the set

$\displaystyle \{ {A^k}x;k = 0,1,2, \cdots ,x\;{\text{is}}\;{\text{quasi - analytic}}\} $

is total in H.

References [Enhancements On Off] (What's this?)

  • [1] E. Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572-615. MR 21 #5901. MR 0107176 (21:5901)
  • [2] A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179-191. MR 33 #3105. MR 0194899 (33:3105)
  • [3] R. S. Phillips, Dissipative operators and hyperbolic systems of partial differential equations, Trans. Amer. Math. Soc. 90 (1959), 193-254. MR 21 #3669. MR 0104919 (21:3669)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0275224-9
Keywords: Quasi-analytic vectors, dissipative operators, contraction semigroups
Article copyright: © Copyright 1971 American Mathematical Society

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