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 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.
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Casti, J. (1979). On the Algebraic Classification of Fredholm Integral Operators. In: Golberg, M.A. (eds) Solution Methods for Integral Equations. Mathematical Concepts and Methods in Science and Engineering, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-1466-1_12
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DOI: https://doi.org/10.1007/978-1-4757-1466-1_12
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