Accession Number : ADA114486

Title :   A Spectral Mapping Theorem for the Exponential Function, and Some Counterexamples.

Descriptive Note : Technical summary rept.,


Personal Author(s) : Kato,Tosio

PDF Url : ADA114486

Report Date : Jan 1982

Pagination or Media Count : 8

Abstract : Elementary proofs are given for the (known) theorems that (1) each point of superscript sigma(A) 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 sigma(A) equal Sigma (e superscript A)/(0) 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)

Descriptors :   *Exponential functions, *Spectra, *Mapping, *Countermeasures, *Linear differential equations, Hilbert space, Operators(Mathematics), Linearity, Banach space, Theory, Spectral lines

Subject Categories : Cartography and Aerial Photography
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE