Abstract
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 theRiccati 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.
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Communicated by M. A. Golberg
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Casti, J. On the algebraic classification of Fredholm integral operators. J Optim Theory Appl 24, 153–167 (1978). https://doi.org/10.1007/BF00933185
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DOI: https://doi.org/10.1007/BF00933185