On the Type of Certain Co-Semigroups
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis Ltd in Communications in Partial Differential Equations
- Vol. 18 (7-8), 1299-1307
- https://doi.org/10.1080/03605309308820975
Abstract
Let be the infinitesimal generator of a Co-semigroup in Hilbert space. We assume that A0 is normal and B is bounded. We further assume that there is M > 0 such that every spectral value of A:O with modulus greater than M - 1 is an isolated eigenvalue with finite multiplicity. Moreover, we assume that the multiplicities of all the eigenvalues lying in any given unit disk (centered at some z with ) do not add up to more than some fixed integer n. It is proved that the type of the semigroup is determined by the spectrum of A. Applications to one-dimensional hyperbolic problems are given.Keywords
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