Accession Number:

ADA114486

Title:

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

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• Kato,Tosio

Report Date:

1982-01-01

Pagination or Media Count:

8.0

Abstract:

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

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