On the algebraic classification of Fredholm integral operators

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.