An Extension of E. Bishop's Localization Theorem
نویسندگان
چکیده
We prove that if f is a function belonging to Baire first class on a compact set K/C and each point of K has a (closed) neighborhood where f is the pointwise limit of some sequence of uniformly bounded rational functions, then f on the whole of K is the pointwise limit of a sequence of rational functions uniformly bounded on K. This is an extension of Bishop's localization theorem. As an application we establish a ``pointwise'' version of Mergelyan's classical theorem on uniform approximation by rational functions on compact sets for which the components of its complement have diameters greater than a fixed positive number. 2001
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 109 شماره
صفحات -
تاریخ انتشار 2001