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Conformal mapping and Fourier-Jacobi approximations

Part of the Lecture Notes in Mathematics book series (LNM,volume 1435)

Abstract

Let f denote the conformal map of a domain interior (exterior) to a closed Jordan curve onto the interior (exterior) of the unit circle. In this paper, we explain how the corner singularities of the of the derivative of the boundary correspondence function can be represented by Jacobi weight functions, and study the convergence properties of an associated Fourier-Jacobi method for approximating this derivative. The practical significance of this work is that some of the best known methods for approximating f are based on integral equations for either the boundary correspondence function or its derivative.

Keywords

  • Conformal Mapping
  • Polynomial Approximation
  • Linear Algebraic System
  • Boundary Integral Formulation
  • Maximum Modulus Principle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

On leave of absence from the Department of Mathematics, Coventry Polytechnic, UK

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© 1990 Springer-Verlag

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Hough, D.M. (1990). Conformal mapping and Fourier-Jacobi approximations. In: Ruscheweyh, S., Saff, E.B., Salinas, L.C., Varga, R.S. (eds) Computational Methods and Function Theory. Lecture Notes in Mathematics, vol 1435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087897

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  • DOI: https://doi.org/10.1007/BFb0087897

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52768-8

  • Online ISBN: 978-3-540-47139-4

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