Abstract
Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields.
For a function analytic in a neighborhood of the origin in the complex plane, we associate a vector field and its dual, an operator version of Fourier transform. The construction extends naturally to functions of several variables.
We illustrate with various examples and present an efficient algorithm readily implemented as a symbolic procedure in Maple while suitable as well for numerical computations using languages such as C or Java.
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References
Feinsilver, P., Schott, R.: Algebraic structures and operator calculus, vol. I–III. Kluwer Academic Publishers, Dordrecht (1993, 1994, 1996)
Feinsilver, P., Schott, R.: Vector fields and their duals. Adv. in Math. 149, 182–192 (2000)
Rota, G.-C., Kahaner, D., Odlyzko, A.: Finite operator calculus. Academic Press, London (1975)
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© 2006 Springer-Verlag Berlin Heidelberg
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Feinsilver, P., Schott, R. (2006). Operator Calculus Approach to Solving Analytic Systems. In: Calmet, J., Ida, T., Wang, D. (eds) Artificial Intelligence and Symbolic Computation. AISC 2006. Lecture Notes in Computer Science(), vol 4120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11856290_16
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DOI: https://doi.org/10.1007/11856290_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-39728-1
Online ISBN: 978-3-540-39730-4
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