Representation of Shift Invariant Operators on L2 by H at Infinity Transfer Functions: An Elementary Proof, a Generalization to L Rho and a Counterexample for L at Infinity

Abstract

An elementary proof is given of the well known fact that shift invariant operators on (L-sq)/0, infinity) are represented by transfer functions which are bounded and analytic on the right open half-plane. Proved is a generalization to Banach space-valued L superscript p functions, where 1 < or = p < infinity. The result no longer holds for p = infinity.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1989
Accession Number
ADA207736

Entities

People

  • George Weiss

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Analytic Functions
  • Applied Mathematics
  • Banach Space
  • Complex Variables
  • Contracts
  • Hilbert Space
  • Intervals
  • Mathematics
  • Notation
  • Scalar Functions
  • Scientific Research
  • Security
  • Step Functions
  • Theorems
  • Transfer Functions
  • Universities

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers