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 study an interesting class of Banach function algebras of innitely dierentiable functions onperfect, compact plane sets. These algebras were introduced by Honary and Mahyar in 1999, calledLipschitz algebras of innitely dierentiable functions and denoted by Lip(X;M; ), where X is aperfect, compact plane set, M = fMng1n=0 is a sequence of positive numbers such that M0 = 1 and(m+n)!Mm+n ( m!Mm)...
متن کاملCompact endomorphisms of Banach algebras of infinitely differentiable functions
Let (Mn) be a sequence of positive numbers satisfying M0 = 1 and Mn+m MnMm ≥ ( n+m n ) , m, n, non-negative integers. We let D([0, 1],M) = {f ∈ C∞([0, 1]) : ‖f‖ = ∞ ∑
متن کاملNormed Algebras of Differentiable Functions on Compact Plane Sets
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...
متن کاملgH-differentiable of the 2th-order functions interpolating
Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1967
ISSN: 0373-0956
DOI: 10.5802/aif.270