Abstract
We present a characterization of hyperbolicity for strongly contin- uous semigroups on Banach spaces in terms of Fourier multiplier properties of the resolvent of the generator. Hyperbolicity with respect to classical solu- tions 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. R¨abiger, T. Randolph, and L. Weis.
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CITATION STYLE
Latushkin, Y., & Shvydkoy, R. (2001). Hyperbolicity of semigroups and Fourier multipliers. In Systems, Approximation, Singular Integral Operators, and Related Topics (pp. 341–363). Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8362-7_14
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