Hyperbolicity of semigroups and Fourier multipliers

Details Hyperbolicity of semigroups and Fourier multipliers Hyperbolicity of semigroups and Fourier multipliers

2001-07-28

arxiv.org/abs/math/0107205v1

Mathematics

Functional Analysis

26 pages

Scientific paper

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. R\"{a}biger, T. Randolph, and L. Weis.

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