BESSEL GENERALIZED TRANSLATIONS AND SOME PROBLEMS OF APPROXIMATION THEORY FOR FUNCTIONS ON THE HALF-LINE

S. S. Platonov

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BESSEL GENERALIZED TRANSLATIONS AND SOME PROBLEMS OF APPROXIMATION THEORY FOR FUNCTIONS ON THE HALF-LINE

机译：贝塞尔广义翻译和半直线上的函数逼近理论的一些问题

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Approximation problems for functions on the half-line [0,+∞) in a weighted Lp-metric are studied with the use of Bessel generalized translation. A direct theorem of Jackson type is proven for the modulus of smoothness of arbitrary order which is constructed on the basis of Bessel generalized translation. Equivalence is stated between the modulus of smoothness and the K-functional constructed by the Sobolev space corresponding to the Bessel differential operator. A particular class of entire functions of exponential type is used for approximation. The problems under consideration are studied mostly by means of Fourier–Bessel harmonic analysis.

机译：使用Bessel广义平移研究了加权Lp度量中半线上[0，+∞）上的函数的逼近问题。证明了基于Bessel广义平移构造的任意阶平滑模量的Jackson型直接定理。光滑度模量和由对应于贝塞尔微分算子的Sobolev空间构造的K函数之间的等价关系。指数类型的整个函数的特定类别用于近似。所考虑的问题主要通过傅里叶-贝塞尔谐波分析来研究。

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《Siberian Mathematical Journal》 |2009年第1期|共18页
作者
S. S. Platonov;
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原文格式 PDF
正文语种 eng
中图分类 510LB010;
关键词
approximation of functions; Jackson theorems; K-functional; Bessel generalized translation; moduli of smoothness; Bessel transforms; entire function of exponential type;

机译：函数逼近;杰克逊定理;K-函数;贝塞尔广义平移;光滑度模量;贝塞尔变换;指数型整函数;

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BESSEL GENERALIZED TRANSLATIONS AND SOME PROBLEMS OF APPROXIMATION THEORY FOR FUNCTIONS ON THE HALF-LINE

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