ISSN:
1432-0940
Keywords:
41 A 20
;
30 E 10
;
Order of approximation
;
Rational functions and electrostatic fields due to distribution of electrons
;
Bers space
;
Jordan domain
;
Conformal mapping
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetD be a Jordan domain in the complex plane andA q (D) the Bers space with norm ∥ ∥ q . IfD is the unit disk, it is known that ∥S n 0∥2≥π/18, whereS n =∑ k=1 n l/(z−z nk ) withz nk ∈∂D, so that approximation in ∥ ∥ q ,q〈-2, is not possible. In this paper, we give an order of estimate of ∥f−S n ∥ q for 2〈q〈∞ when ∂D is a sufficiently smooth Jordan curve, and prove that this order of approximation is in general best possible.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01890026
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