J. Falcó, P. Gauthier, Myrto Manolaki, V. Nestoridis
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引用次数: 0
摘要
在Gauthier, Manolaki, and Nestoridis (2021, Advances In Mathematics 381, 107649)中，为了纠正Gamelin and Garnett (1969, Transactions of American Mathematical Society 143, 187-200)关于紧集K在$\mathbb C^d$上一致逼近的一个错误的Mergelyan-type陈述，作者引入了一个比经典函数代数$ a (K)$小的自然函数代数$A_D(K)$。在本文中，我们研究了这两个代数重合的情况，并将它们与包含紧集K的开集上的多项式、有理函数或全纯函数的所有似似逼近函数的类进行了比较。最后，我们引入了K的o壳的概念，并加强了已知的结果。
Some remarks on approximation in several complex variables
Abstract In Gauthier, Manolaki, and Nestoridis (2021, Advances in Mathematics 381, 107649), in order to correct a false Mergelyan-type statement given in Gamelin and Garnett (1969, Transactions of the American Mathematical Society 143, 187–200) on uniform approximation on compact sets K in
$\mathbb C^d$
, the authors introduced a natural function algebra
$A_D(K)$
which is smaller than the classical one
$A(K)$
. In the present paper, we investigate when these two algebras coincide and compare them with the classes of all plausibly approximable functions by polynomials or rational functions or functions holomorphic on open sets containing the compact set K. Finally, we introduce a notion of O-hull of K and strengthen known results.
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