Resolvent Kernels of Green's Function Kernels and Other Finite Rank Modifications of Fredholm and Volterra Kernels.

Abstract

Many important Fredholm integral equations have separable kernels, which are finite rank modifications of Volterra kernels. This class of kernels includes Green's functions for Sturm-Liouville and other two-point boundary value problems for linear ordinary differential operators. It is shown how to construct the Fredholm determinant, resolvent kernel, and eigenfunctions of kernels of this class by solving related Volterra integral equations and finite linear algebraic systems. Applications to boundary value problems are discussed and explicit formulas are given for a simple example. Analytic and numerical approximation procedures for more general problems are indicated. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1976
Accession Number
ADA031947

Entities

People

  • Louis B. Rall

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Construction
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Identities
  • Integral Equations
  • Integrals
  • Mathematics
  • New York
  • Numerical Analysis
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.