DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click HERE
to register or log in.
A Spectral Mapping Theorem for the Exponential Function, and Some Counterexamples.
Technical summary rept.,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
Elementary proofs are given for the known theorems that 1 each point of superscript sigmaA belongs to superscript sigma e superscript A if A is the generator of a C sub 0-semigroup E superscript tA of linear operators on a Banach space x, and that 2 e superscript sigmaA equal Sigma e superscript A0 if e superscript tA is a holomorphic semigroup. Also a large class of strongly continous groups e superscript tA on a Hilbert space H is given such that Sigma A is empty. Note that Sigma e superscript A is not empty, and is away from zero, if e superscript tA is a group. Some related remarks are given on the relationship between the spectral bound of A and the type of e superscript tA. Author
APPROVED FOR PUBLIC RELEASE