Hyperbolicity of semigroups and Fourier multipliers

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We present a characterization of hyperbolicity for strongly continuous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hyperbolicity with respect to classical solutions is also considered. Our approach unifies and simplifies the M. Kaashoek-- S. Verduyn Lunel theory and multiplier-type results previously obtained by S. Clark, M. Hieber, S. Montgomery-Smith, F. Räbiger, T. Randolph, and L. Weis.
26 pages

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Functional Analysis, Primary: 47D06; Secondary: 42B15

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http://salesiana.dossiersoluciones.com/handle/123456789/61923

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0107205
 http://arxiv.org/abs/math/0107205

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arXiv