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Approximation in Lipschitz algebras of infinitely differentiable functions. (English) Zbl 0951.46025
Summary: We introduce Lipschitz algebras of differentiable functions on a perfect compact plane set X and then extend the definition to Lipschitz algebras of infinitely differentiable functions on X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.
MSC:
46J10Banach algebras of continuous functions, function algebras
46J15Banach algebras of differentiable or analytic functions, H p -spaces
46J20Ideals, maximal ideals, boundaries of commutative topological algebras
41A10Approximation by polynomials
41A20Approximation by rational functions