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Lip 1 Rational Approximation
Author(s) -
O'Farrell Anthony G.
Publication year - 1975
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-11.2.159
Subject(s) - disjoint sets , mathematics , limit (mathematics) , simple (philosophy) , sequence (biology) , rational function , norm (philosophy) , pure mathematics , function (biology) , plane (geometry) , limit of a sequence , superposition principle , combinatorics , mathematical analysis , discrete mathematics , geometry , chemistry , philosophy , epistemology , evolutionary biology , political science , law , biology , biochemistry
Let X be a compact subset of the complex plane C. We prove that every C 1 function is the limit in Lip (1, X ) norm of a sequence of rational functions if and only if X is a subset of a finite union of disjoint simple C 1 curves.