Construction of Polynomials of a Special Kind and Examples of Their Application in the Theory of Power Series and in the Wavelet Theory

E. V. Mishchenko

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Construction of Polynomials of a Special Kind and Examples of Their Application in the Theory of Power Series and in the Wavelet Theory

机译：特殊类型多项式的构造及其在幂级数理论和小波理论中的应用实例

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In this paper we construct polynomials of a special type. We consider examples of their application for studying the convergence of special power series, for determining the upper and lower Riesz bounds for a basis consisting of B-splines, and for studying the convergence of a sequence of Battle–Lemarie′ scaling functions.

机译：在本文中，我们构造了一种特殊类型的多项式。我们考虑其在研究特殊幂级数的收敛性，确定由B样条曲线组成的基础上的Riesz上下边界以及研究Battle-Lemarie'标度函数序列的收敛性的示例。

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《Russian mathematics》 |2011年第1期|共14页
作者
E. V. Mishchenko;
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正文语种 eng
中图分类数学;
关键词
functional series; B-splines; Riesz basis; Battle–Lemarie scaling function; Shennon–Kotel’nikov function;

机译：函数级数;B样条;Riesz基;Battle–Lemarie缩放函数;Shennon–Kotel’nikov函数;

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Construction of Polynomials of a Special Kind and Examples of Their Application in the Theory of Power Series and in the Wavelet Theory

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