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Type: Journal article
Title: On the Favard classes of semigroups associated with pseudo-resolvents
Author: Chojnacki, W.
Kisynski, J.
Citation: Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum, 1998; 64(3-4):681-696
Publisher: Acta Universitatis Szegediensis
Issue Date: 1998
ISSN: 0001-6969
Statement of
Wojciech Chojnacki and Jan Kisyński
Abstract: A pseudo-resolvent on a Banach space, indexed by positive numbers and tempered at infinity, gives rise to a bounded strongly continuous one-parameter semigroup S on a closed subspace of the ambient Banach space. We prove that the range space of the pseudo-resolvent contains the domain of the generator of S, and is contained in the Favard class of S, which consists of all uniformly Lipschitz vectors for S. We explore when some or all of these three spaces coincide.
Keywords: Favard class
one-parameter semigroup
uniformly Lipschitz vector
Rights: © Bolyai Institute, University of Szeged
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