On approximation by trigonometrical polynomials in $L_2$ space
نویسندگان
چکیده
منابع مشابه
On the approximation by {polynomials
As usual, p∗ is called a best approximation (b.a.) to f in (or, by elements of) IPγ,n. To give some examples, let X = Lp[0, 1] and set γ(t) = G(·, t), where G(s, t) is defined on [0, 1] × T . With G Green’s function for a k–th order ordinary linear initial value problem on (0, 1] and T = [0, 1), one has approximation by generalized splines. With G(s, t) = e and T = IR, one has approximation by ...
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These notes are prepared as lecture notes exclusively for the participants of this conference only. Any reproduction in any media, or any use for any other purpose of any part of this manuscript, without an expressed written consent of the author is unlawful.thorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conc...
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1. Let In ;) be a set of distinct positive integers. According to a theorem of Müntz and Szász, the condition En-' .' =-is necessary and sufficient in order that polynomials in the powers x"' and 1 suffice to approximate uniformly an arbitrary continuous function in the interval 0 < x < 1, i .e ., that these powers span the space C of continuous functions in that interval. If the series converg...
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ژورنال
عنوان ژورنال: Researches in Mathematics
سال: 2016
ISSN: 2664-5009,2664-4991
DOI: 10.15421/241614