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# 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

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#