ENTIRE SOLUTIONS OF THE ABSTRACT CAUCHY-PROBLEM IN A HILBERT-SPACE

Authors
DELAUBENFELS R YAO FY
Citation
R. Delaubenfels et Fy. Yao, ENTIRE SOLUTIONS OF THE ABSTRACT CAUCHY-PROBLEM IN A HILBERT-SPACE, Proceedings of the American Mathematical Society, 123(11), 1995, pp. 3351-3356
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
11
Year of publication
1995
Pages
3351 - 3356
Database
ISI
SICI code
0002-9939(1995)123:11<3351:ESOTAC>2.0.ZU;2-Q
Abstract
We show that, whenever the linear operator A is symmetric and densely defined, on a Hilbert space, then the abstract Cauchy problem d/dz u(z ) = A(u(z)) (z is an element of C), u(0) = x has an entire solution, for all initial data x in the image of e(-<(A)over bar A>), which is a dense set.