Citation
W. Arendt et al., Functional calculus, variational methods and Liapunov's theorem, ARCH MATH, 77(1), 2001, pp. 65-75
Citations number
20
Categorie Soggetti
Mathematics
Journal title
ARCHIV DER MATHEMATIK
ISSN journal
0003889X
→ ACNP
Volume
77
Issue
1
Year of publication
2001
Pages
65 - 75
Database
ISI
SICI code
0003-889X(20010701)77:1<65:FCVMAL>2.0.ZU;2-0
Abstract
Given the generator -A of a holomorphic semigroup on a Hilbert space H, we
show that A is associated with a closed form if and only if A + w is an ele
ment of BIP(H) for some w is an element of R. Under this condition we also
show that Liapunov's classical theorem is true, in the linear as well as th
e semilinear case.