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

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)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1982
Accession Number
ADA114486

Entities

People

  • Tosio Kato

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Banach Space
  • Complex Numbers
  • Contracts
  • Differential Equations
  • Eigenvalues
  • Equations
  • Exponential Functions
  • Generators
  • Hilbert Space
  • Integrals
  • Linear Differential Equations
  • Mathematics
  • North Carolina
  • Numbers
  • Partial Differential Equations
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Materials Science and Engineering.

Technology Areas

  • Space