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Approximation in Lipschitz algebras. (English) Zbl 0963.46034

The authors study the Lipschitz algebras \(L^p(X,\alpha)\) and \(\text{lip}(X,\alpha)\) for a compact subset \(X\in \mathbb{C}^n.\) They investigate the maximal ideal spaces for subalgebras of these algebras, generated by rational functions or by functions analytic in the interior of \(X.\) Approximation by rational functions is studied also.

MSC:

46J10 Banach algebras of continuous functions, function algebras
41A20 Approximation by rational functions
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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