On quasi-analytic vectors for dissipative operators
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- by Minoru Hasegawa PDF
- Proc. Amer. Math. Soc. 29 (1971), 81-84 Request permission
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 \[ \{ {A^k}x;k = 0,1,2, \cdots ,x\;{\text {is}}\;{\text {quasi - analytic}}\} \] is total in H.References
- Edward Nelson, Analytic vectors, Ann. of Math. (2) 70 (1959), 572–615. MR 107176, DOI 10.2307/1970331
- A. E. Nussbaum, Quasi-analytic vectors, Ark. Mat. 6 (1965), 179–191 (1965). MR 194899, DOI 10.1007/BF02591357
- R. S. Phillips, Dissipative operators and hyperbolic systems of partial differential equations, Trans. Amer. Math. Soc. 90 (1959), 193–254. MR 104919, DOI 10.1090/S0002-9947-1959-0104919-1
Additional Information
- © Copyright 1971 American Mathematical Society
- 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