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ArticleOriginal scientific text

Title

On analytic semigroups and cosine functions in Banach spaces

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931
  2. Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany

Abstract

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.

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Studia Mathematica
1998/129/2
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Pages:
137-156
Main language of publication
English
Received
1996-12-30
Accepted
1997-06-09
Published
1998
Exact and natural sciences