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Proceedings of the American Mathematical Society

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A remark on the abstract Cauchy problem on spaces of Hölder continuous functions


Authors: Matthias Hieber and Frank Räbiger
Journal: Proc. Amer. Math. Soc. 115 (1992), 431-434
MSC: Primary 47D03; Secondary 34G10, 47D06
DOI: https://doi.org/10.1090/S0002-9939-1992-1092921-X
MathSciNet review: 1092921
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Abstract: We prove that the generator of a $ {C_0}$-semigroup on $ {C^\alpha }({\mathbb{R}^n})$ is a bounded operator. Nevertheless, certain elliptic differential operators generate $ \beta $-times integrated semigroups on $ {C^\alpha }({\mathbb{R}^n})$ whenever $ \beta > n/2 + 1$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1092921-X
Article copyright: © Copyright 1992 American Mathematical Society