On the Algebraic Classification of Fredholm Integral Operators

  • J. Casti
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 18)


Using the well-known and specific connections between Fredholm integral equations, two-point boundary-value problems, and linear dynamics—quadratic cost control processes, we present a complete, independent set of algebraic invariants suitable for classifying a wide range of Fredholm integral operators with respect to a certain group of transformations. The group, termed the Riccati group, is naturally suggested by the control theoretic setting, but seems nonintuitive from a purely integral-equations point of view. Computational considerations resulting from this classification are discussed.


Riccati Equation Fredholm Integral Equation Algebraic Riccati Equation Algebraic Invariant Matrix Riccati Equation 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • J. Casti
    • 1
  1. 1.Department of Computer Applications and Information Systems, and Department of Quantitative AnalysisNew York UniversityNew YorkUSA

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