Completions of normed algebras of differentiable functions
نویسندگان
چکیده
منابع مشابه
Completions of normed algebras of differentiable functions
In this paper we look at normed spaces of differentiable functions on compact plane sets, including the spaces of infinitely differentiable functions considered by Dales and Davie in [7]. For many compact plane sets the classical definitions give rise to incomplete spaces. We introduce an alternative definition of differentiability which allows us to describe the completions of these spaces. We...
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We investigate the completeness and completions of the normed algebras (D(1)(X), ‖ · ‖) for perfect, compact plane sets X. In particular, we construct a radially self-absorbing, compact plane set X such that the normed algebra (D(1)(X), ‖ · ‖) is not complete. This solves a question of Bland and Feinstein. We also prove that there are several classes of connected, compact plane sets X for which...
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The notation and terminology used here have been introduced in the following papers: [12], [2], [3], [7], [9], [11], [1], [4], [10], [13], [6], [17], [18], [15], [8], [16], [19], and [5]. For simplicity, we adopt the following rules: F denotes a non trivial real normed space, G denotes a real normed space, X denotes a set, x, x0, r, p denote real numbers, n, k denote elements of N, Y denotes a ...
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From now on S, T ,W , Y denote real normed spaces, f , f1, f2 denote partial functions from S to T , Z denotes a subset of S, and i, n denote natural numbers. Now we state the propositions: (1) Let us consider a set X and functions I, f . Then (f X) · I = (f · I) I−1(X). (2) Let us consider real normed spaces S, T , a linear operator L from S into T , and points x, y of S. Then L(x)− L(y) = L(x...
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In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vectorvalued functio...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2005
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm170-1-5