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Kronecker’s approximation theorem
Indagationes Mathematicae, 2016 By elementary algebraic/arithmetic reasoning \textit{L. Kronecker} [Berl. Ber. 1884, 1179--1193 (1884; JFM 16.0083.02)] proved: Theorem A. Let \(A\) be an \(N \times M\) matrix with real entries, and let \(\alpha\in \mathbb R^N\) . Then the following two assertions are equivalent: 1.
Steven M. Gonek, Hugh L. Montgomery
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THE BLOCK APPROXIMATION THEOREM [PDF]
, 2013 The block approximation theorem is an extensive general- ization of both the well known weak approximation theorem from valu- ation theory and the density property of global fields in their henseliza- tions. It guarantees the existence of rational points
Pop, Florian, Haran, Dan, Jarden, Moshe
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The Weierstrass theorem on polynomial approximation [PDF]
, 1981 summary:In the paper a simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given.
Výborný, Rudolf +2 more
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Approximation properties of λ-Bernstein operators
Journal of Inequalities and Applications, 2018 In this paper, we introduce a new type λ-Bernstein operators with parameter λ∈[−1,1] $\lambda\in[-1,1]$, we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz ...
Qing-Bo Cai, Bo-Yong Lian, Guorong Zhou
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On ( p , q ) $(p,q)$ -analogue of two parametric Stancu-Beta operators
Journal of Inequalities and Applications, 2016 Our purpose is to introduce a two-parametric ( p , q ) $(p, q)$ -analogue of the Stancu-Beta operators. We study approximating properties of these operators using the Korovkin approximation theorem and also study a direct theorem.
Mohammad Mursaleen +2 more
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A Formalisation of Gallagher’s Ergodic Theorem [PDF]
, 2023 Gallagher’s ergodic theorem is a result in metric number theory. It states that the approximation of real numbers by rational numbers obeys a striking "all or nothing" behaviour. We discuss a formalisation of this result in the Lean theorem prover.
Nash, Oliver
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Asian Journal of Mathematics, 2015 The theme of this thesis is an "approximate converse theorem" for globally unramified cuspidal representations of PGL(n, A), n ≥ 1. For a given set of Langlands parameters for some places of Q, we can compute ε > 0 such that there exists a genuine globally unramified cuspidal representation, whose Langlands parameters are within ε of the given ones ...
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The Weierstrass theorem on polynomial approximation [PDF]
Mathematica Bohemica, 2005 Summary: A simple proof of the Weierstrass approximation theorem on a function continuous on a compact interval of the real line is given. The proof is elementary in the sense that it does not use uniform continuity.
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Rate of convergence in Trotter's approximation theorem
, 2008 We give a quantitative estimate of the convergence in Trotter's approximation theorem on the convergence of iterates of linear operators to an assigned semigroup.
TACELLI, CRISTIAN +3 more
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Journal of Kufa for Mathematics and Computer, 2017 For a given nonnegative integer number n, we can find a monotone function f depending on n, defined on the interval I=[-1,1], and an absolute constant c>0, satisfying the following relationship: (2〖E_n (f Ì )〗_p)/(n+1)^3 ≤〖E_(n+1)^1 (f)〗_pâ ...
GHAZI ABDULLAH Madlol
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