منابع مشابه
On Hilbert Extensions of Weierstrass’ Theorem with Weights
Abstract. In this paper we study the set of functions G-valued which can be approximated by G-valued continuous functions in the norm L∞G (I, w), where I is a compact interval, G is a real and separable Hilbert space and w is certain G-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem. Also, we characterize the set of functions whic...
متن کاملGeneralized Wronskians and Weierstrass Weights
Given a point P on a smooth projective curve C of genus g, one can determine the Weierstrass weight of that point by looking at a certain Wronskian. In practice, this computation is difficult to do for large genus. We introduce a natural generalization of the Wronskian matrix, which depends on a sequence of integers s = m0, . . . ,mg−1 and show that the determinant of our matrix is nonzero at P...
متن کاملThe Stone-weierstrass Theorem
The really new thing about Stone’s approach to the approximation theorem was the approach via lattices of continuous functions, although Lebesgue had noticed the importance of approximating the absolute-value function earlier. There is a segment of the mathematical community formed of people who are as likely to encounter a lattice in their work as an algebra and for whom the lattice version of...
متن کاملThe Theorem of Weierstrass
The basic purpose of this article is to prove the important Weier-strass' theorem which states that a real valued continuous function f on a topological space T assumes a maximum and a minimum value on the compact subset S of T , i.e., there exist points x1, x2 of T being elements of S, such that f(x1) and f(x2) are the supremum and the innmum, respectively, of f(S), which is the image of S und...
متن کاملAn Effective Weierstrass Division Theorem
We prove an effective Weierstrass Division Theorem for algebraic restricted power series with p-adic coefficients. The complexity of such power series is measured using a certain height function on the algebraic closure of the field of rational functions over Q. The paper includes a construction of this height function, following an idea of Kani. We apply the effective Weierstrass Division Theo...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2004
ISSN: 0021-9045
DOI: 10.1016/j.jat.2004.01.003