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Equibounded pointwise approximation implies the uniform one
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DOI：10.1007/s13324-026-01202-w.png)
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Abstract
En 中文
Given any compact Hausdorff space X, we present a simple proof that a continuous function g is an element of C(X) can be uniformly approximated on X by elements of some linear subspace L subset of C(X), if and only if g can be pointwise approximated on X by some equibounded sequence in L. Moreover, given any compactum K subset of C, we also show that every f is an element of C(K) can be uniformly approximated by rational functions (without poles on K), if and only if the complex conjugate w -> w(-) can be pointwise approximated by functions holomorphic on K (no equibounded hypothesis required).
Keywords:
Pointwise and uniform approximations
Equibounded
Holomorphic polynomials
Rational functions
Journal
A
IF:
1.6
Papers:
76
Citations:
0