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Initial value methods in the theory of Fredholm integral equations

Abstract

This paper deals with the problem of establishing the equivalence of a family of integral equations of Fredholm type with kernels that depend on a parameter λ and a related Cauchy system of integrodifferential equations. We also show how the Cauchy problem can be given an abstract formulation as an initial value problem in a complex Banach space.

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References

  1. 1.

    Kalaba, R. E., andRuspini, E.,Reduction of the Dirichlet Problem to an Initial Value Problem, University of Southern California, Technical Report, 1970.

  2. 2.

    Kalaba, R. E., andZagustin, E.,Reduction of Fredholm Integral Equations To Cauchy Systems, University of Southern California, Technical Report, 1970.

  3. 3.

    Lovitt, V.,Linear Integral Equations, Dover Publications, New York, 1950.

  4. 4.

    Dieudonne, J.,Foundations of Modern Analysis, Academic Press, New York, 1960.

Additional Bibliography

  1. 51.

    Casti, J., Kalaba, R. E., andScott, M.,A Proposal for the Calculation of Characteristic Functions for Certain Differential and Integral Operators Via Initial-Value Procedures, The RAND Corporation, Research Memorandum No. RM-6164-PR, 1970.

  2. 6.

    Kagiwada, H. H., Kalaba, R. E., andShumitzky, A.,Differential Systems for Eigenvalues of Fredholm Integral Equations, The RAND Corporation, Research Memorandum No. RM-5361-PR, 1967.

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Additional information

This research was supported by the University of Nevada at Las Vegas, Research Grant No. 4503.

Communicated by R. E. Kalaba

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Golberg, M.A. Initial value methods in the theory of Fredholm integral equations. J Optim Theory Appl 9, 112–119 (1972). https://doi.org/10.1007/BF00932348

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Keywords

  • Banach Space
  • Integral Equation
  • Cauchy Problem
  • Abstract Formulation
  • Fredholm Integral Equation