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Operator Calculus Approach to Solving Analytic Systems

  • Philip Feinsilver
  • René Schott
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4120)

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

  1. 1.
    Feinsilver, P., Schott, R.: Algebraic structures and operator calculus, vol. I–III. Kluwer Academic Publishers, Dordrecht (1993, 1994, 1996)zbMATHGoogle Scholar
  2. 2.
    Feinsilver, P., Schott, R.: Vector fields and their duals. Adv. in Math. 149, 182–192 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Rota, G.-C., Kahaner, D., Odlyzko, A.: Finite operator calculus. Academic Press, London (1975)zbMATHGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Philip Feinsilver
    • 1
  • René Schott
    • 2
  1. 1.Southern Illinois UniversityCarbondaleU.S.A.
  2. 2.Université Henri Poincaré-Nancy 1Vandoeuvre-lès-NancyFrance

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