International Journal of Mathematics and Mathematical Sciences
The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation of the operational calculus of Fliess for computing the output response of an analytic nonlinear system. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
Original Publication Citation
Li, Y., & Gray, W. S. (2006). The formal Laplace-Borel transform of Fliess operators and the composition product. International Journal of Mathematics and Mathematical Sciences, 2006, 34217. doi:10.1155/IJMMS/2006/34217
Li, Yaqin and Gray, W. Steven, "The Formal Laplace-Borel Transform of Fliess Operators and the Composition Product" (2006). Electrical & Computer Engineering Faculty Publications. 81.