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1998 | 129 | 2 | 137-156
Tytuł artykułu

On analytic semigroups and cosine functions in Banach spaces

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If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform.
Słowa kluczowe
  • Department of Mathematics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931
  • Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany
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