Integrals and Transforms in Function Space.

Abstract

A unified theory that includes ordinary calculus, theory of differential equations and theory of stochastic differential equations has been developed. Problems relating to classifying probability space were studied. Necessary and sufficient conditions were found for the operator equation BX-XA=Q, where B, A are self-adjoint operators in the space, beta(H), of bounded operators on a complex Hilbert space, Q belongs to beta(H), to have a solution in beta (H). Research on resonance problems focused on the question of the meaning, interpretation, and approximation of resonances (i.e., poles of a continued resolvent on S-matrix.) Gaussian processes, especially such processes in which the time parameter was in Euclidean n-space were studied. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1973
Accession Number
AD0756505

Entities

People

  • E. J. Mcshane

Organizations

  • University of Virginia

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Calculus
  • Differential Equations
  • Equations
  • Gaussian Processes
  • Hilbert Space
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Probability
  • Real Variables
  • Resonance

Readers

  • Linear Algebra
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space