Compact Covariance Operators.

Abstract

The study of covariance operators is a major component in the theory of probability measures on Banach spaces. The covariance operators of a strong second-order measure is always compact however, the covariance operator of a weak second-order measure need not be compact. In this paper we first characterize series representations of covariance operators, and then give a set of necessary and sufficient conditions for a covariance operator to be compact. The classical Mercer's theorem can be obtained as an immediate corollary. These results are then applied to extend a result of Prohorov and Sazanov on relative compactness of probability measures from Hilbert space to Banach space.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1981
Accession Number
ADA105658

Entities

People

  • Charles R. Baker
  • Ian W. Mckeague

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Computing-Related Activities
  • Convergence
  • Covariance
  • Data Science
  • Eigenvectors
  • Hilbert Space
  • Information Science
  • Military Research
  • North Carolina
  • Plastic Explosives
  • Probability
  • Statistics
  • Topology
  • Vector Spaces
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Statistical inference.

Technology Areas

  • Space