-Convergence of Finite Element Approximation
J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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Włodzimierz Łenski, Bogdan Roszak (2011)
Banach Center Publications
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We present an estimation of the and means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.
Eve Oja, Silja Treialt (2013)
Studia Mathematica
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The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
Hichame Amal (2014)
Annales Polonici Mathematici
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Our aim in this article is the study of subextension and approximation of plurisubharmonic functions in , the class of functions with finite χ-energy and given boundary values. We show that, under certain conditions, one can approximate any function in by an increasing sequence of plurisubharmonic functions defined on strictly larger domains.
Wiesław Krajewski, Umberto Viaro (2018)
Kybernetika
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A computationally simple method for generating reduced-order models that minimise the norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the -optimal approximation. Two examples taken from the relevant literature show that the suggested techniques...
Carsten Elsner (2006)
Colloquium Mathematicae
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We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function can be approximated with arbitrary accuracy by an infinite sum of analytic functions , each solving the same system of universal partial differential equations, namely (σ = 1,..., s).
P. Chandra (1988)
Matematički Vesnik
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Yu. A. Brudnyi, I. E. Gopengauz (2013)
Studia Mathematica
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The main result of the paper estimates the asymptotic behavior of local polynomial approximation for functions at a point via the behavior of μ-differences, a generalization of the kth difference. The result is applied to prove several new and extend classical results on pointwise differentiability of functions including Marcinkiewicz-Zygmund’s and M. Weiss’ theorems. In particular, we present a solution of the problem posed in the 30s by Marcinkiewicz and Zygmund.
WŁodzimierz Łenski, Bogdan Szal (2011)
Banach Center Publications
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We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.
Damien Roy (2013)
Annales de l’institut Fourier
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A point with coordinates in a subfield of of transcendence degree one over , with linearly independent over , may have a uniform exponent of approximation by elements of that is strictly larger than the lower bound given by Dirichlet’s box principle. This appeared as a surprise, in connection to work of Davenport and Schmidt, for points of the parabola . The goal of this paper is to show that this phenomenon extends to all real conics defined over , and that the largest...
S. V. Konyagin, V. N. Temlyakov (2003)
Studia Mathematica
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We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...
Yann Bugeaud (2014)
Publications mathématiques de Besançon
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The Littlewood conjecture in Diophantine approximation claims that holds for all real numbers and , where denotes the distance to the nearest integer. Its -adic analogue, formulated by de Mathan and Teulié in 2004, asserts that holds for every real number and every prime number , where denotes the -adic absolute value normalized by . We survey the known results on these conjectures and highlight recent developments. ...
Yann Bugeaud (2015)
Acta Arithmetica
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Let d be a positive integer and α a real algebraic number of degree d + 1. Set . It is well-known that , where ||·|| denotes the distance to the nearest integer. Furthermore, for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that for any integer n ≥ 1.
Mohammad Mursaleen, Ahmed A. H. Alabied (2018)
Mathematica Bohemica
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We introduce modified -Bernstein-Durrmeyer operators. We discuss approximation properties for these operators based on Korovkin type approximation theorem and compute the order of convergence using usual modulus of continuity. We also study the local approximation property of the sequence of positive linear operators and compute the rate of convergence for the function belonging to the class .
Michal Johanis (2015)
Commentationes Mathematicae Universitatis Carolinae
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We show that a -smooth mapping on an open subset of , , can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.
A. Szankowski (2009)
Journal of the European Mathematical Society
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It is shown that there is a subspace of for which is isomorphic to such that does not have the approximation property. On the other hand, for there is a subspace of such that does not have the approximation property (AP) but the quotient space is isomorphic to . The result is obtained by defining random “Enflo-Davie spaces” which with full probability fail AP for all and have AP for all . For , are isomorphic to .