Non-tangential Limits and Bounded Point Derivations on <mml:msup>R2</mml:msup>(X)

被引：0
|
作者：
Deterding, Stephen [1 ]
机构：
[1] Marshall Univ, Dept Math, Huntington, WV 25755 USA
来源：
COMPLEX ANALYSIS AND OPERATOR THEORY | 2024年 / 18卷 / 03期
关键词：
Point derivation; Rational approximation; <mml:msup>L<mml:mn>2</mml:mn></mml:msup> space; Non-tangential; Interior cone; 30E10; 30H99; 30D40;
D O I：
10.1007/s11785-024-01486-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study L2 approximations of rational functions on the complex plane, focusing on bounded point derivations. We show that if there is a bounded point derivation at x and {xn} is a sequence of points that converges non-tangentially to x, then the sequence of derivatives {f ' (xn)} is uniformly bounded for a large class of functions, specifically those functions which can be approximated by rational functions with poles off X in the L2 norm. A counterexample is constructed that shows that the hypothesis of non-tangential convergence cannot be removed.
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页数：14
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