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The operator $a(x)\frac {d}{dx}$ on Banach space

Author: Fuyuan Yao
Journal: Proc. Amer. Math. Soc. 125 (1997), 1027-1032
MSC (1991): Primary 47D05
MathSciNet review: 1346993
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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.

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Additional Information

Fuyuan Yao
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701

Received by editor(s): January 31, 1995
Received by editor(s) in revised form: July 19, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society

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