urysohn型积分算子下\(L_p\)球的像和积分漏斗的逼近

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2023-04-13 DOI:10.1134/S0016266322040050

A. Huseyin, N. Huseyin, Kh. G. Guseinov

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引用次数: 0

摘要

考虑了在urysohn型积分算子下，空间\(L_p\), \(p>1\)中封闭球的图像和积分漏斗的近似。将空间\(L_p\), \(p>1\)中的闭球替换为由有限个分段常数函数组成的集合，并证明了在适当的离散参数下，这些分段常数函数的像形成了闭球像的内近似。将此结果应用于urysohn型积分算子下空间\(L_p\), \(p>1\)中封闭球的积分漏斗用有限个数的点组成的集合进行近似。

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Approximations of the Images and Integral Funnels of the \(L_p\) Balls under a Urysohn-Type Integral Operator

Approximations of the image and integral funnel of a closed ball of the space \(L_p\), \(p>1\), under a Urysohn-type integral operator are considered. A closed ball of the space \(L_p\), \(p>1\), is replaced by a set consisting of a finite number of piecewise constant functions, and it is proved that, for appropriate discretization parameters, the images of these piecewise constant functions form an internal approximation of the image of the closed ball. This result is applied to approximate the integral funnel of a closed ball of the space \(L_p\), \(p>1\), under a Urysohn-type integral operator by a set consisting of a finite number of points.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.