Simultaneous Approximation by a Polynomial and its Derivatives
نویسندگان
چکیده
منابع مشابه
Simultaneous Approximation by a Polynomial and Its Derivatives
Theorem. If fo is a continuous function on a compact set C without interior and with connected complement of the complex plane, and if fi, • • ■ i fn are continuous functions on a compact totally disconnected subset E of C, then there exists a sequence {pi} of polynomials such that pi-^fo uniformly on C as i—* , and pim—*fk uniformly on E as i—>», for lslk^n, where pi[k] is the kth derivativ...
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The work on the theory of approximations initiated by Weierstrass and continued by Walsh, Keldysh, and Lavrentiev, among others, has culminated in the following theorem of Mergelyan (See Mergelyan [3]): Given any compact subset C of the complex plane, which does not separate the plane, and given any continuous function/on C which is analytic interior to C, then/can be approximated uniformly on ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1959
ISSN: 0002-9939
DOI: 10.2307/2033468