The operator $a(x)\frac {d}{dx}$ on Banach space
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- Proc. Amer. Math. Soc. 125 (1997), 1027-1032 Request permission
Abstract:
The operator $a(x)\frac {d}{dx}$ on $C(I)$, where $I$ is an interval contained in the real line, is considered in many places. In this paper, we attempt to reconsider it in the subspace of $C_0(-\infty ,\infty )$ containing all even functions, and show that it generates a strongly continuous semigroup. It is interesting that our main conditions seem contradictory to previous ones. It is due to the symmetry of the functions and the different domain of the operator than usual.References
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Additional Information
- Fuyuan Yao
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- Email: fyao@ncms1.cb.lucent.com
- Received by editor(s): January 31, 1995
- Received by editor(s) in revised form: July 19, 1995
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1027-1032
- MSC (1991): Primary 47D05
- DOI: https://doi.org/10.1090/S0002-9939-97-03564-8
- MathSciNet review: 1346993