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On Approximation by Rational Functions of Class L1

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Complex Analysis
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Abstract

Let S = {z k }, 0 ≤ |z 1|≤ |z 2|≤…, be a countably infinite set in the complex plane ℂ with no limit points in ℂ. We denote by B S the collection of functions f(z), analytic in ℂ\S, possessing finite L 1 norm,

$$ \parallel f\parallel = \iint\limits_C {|f(z)|}dxdy < \infty \qquad (z = x + iy). $$

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References

  1. L. Bers, “An approximation theorem”, J. Analyse Math. 14 (1965), 1–4.

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  2. Edgar Reich, “L 1-approximation of meromorphic functions”, J. Approximation Theory 31 (1981), 1–5.

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  3. Edgar Reich and Kurt Strebel, “Quasiconformal mappings of the punctured plane”, Springer Lecture Notes in Math., 103 (1983), 182–212.

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  4. Kurt Strebel, “On the existence of extremal Teichmuller mappings”, Complex Variables 9 (1987), 287–295.

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© 1988 Birkhäuser Verlag Basel

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Reich, E. (1988). On Approximation by Rational Functions of Class L1 . In: Hersch, J., Huber, A. (eds) Complex Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9158-5_18

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  • DOI: https://doi.org/10.1007/978-3-0348-9158-5_18

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-1958-8

  • Online ISBN: 978-3-0348-9158-5

  • eBook Packages: Springer Book Archive

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