On Abstract Linear Evolution Equations, I

✍ Scribed by Hagen Neidhardt

• Publisher: John Wiley and Sons
• Year: 1981
• Tongue: English
• Weight: 720 KB
• Volume: 103
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19811030117

✦ Synopsis

Linear Evolution Equations, I

By HAGEN NEIDHARDT of Berlin (Eingegangen am 10. 12. 1980)

I. Introductioii

This paper is concerned with the theory of strongly continuous propagators on an arbitrary BANACH space. The basic idea of our paper goes back to a paper by J. S. HOWLAND [ 13. He found a beautiful one-to-one correspondence between the set of all measurable propagators on a HILBERT space and the set of all evolution groups. This correspondence was generalized to an analogous situation on a separable BANACH space by D. E. EVANS [ Z ] . \Ye give a further generalization of this result to an arbitrary BANACH space. This means we show the existence of one-toone correspondence between a certe'n set of evolution semigroups of class C , and the set of all strongly continuous propagators.

With the help of these results in a further puplication we want to propose a new method to solve linear evolution equations of the type du