Urysohn型积分算子下$L_p$球的象和积分漏斗的逼近
Approximations of the Image and Integral Funnel of the $L_p$ Ball under Urysohn Type Integral Operator
摘要：
研究了空间$L_p,$ $p>1,$的闭球在Urysohn型积分算子下的象和积分漏斗的逼近.空间$L_p,$ $p>1,$的闭球被有限个分段常数函数组成的集合所取代，并证明了在适当指定的离散化参数下，定义的分段常数函数的图像形成闭球图像的内部近似.应用这一结果，在Urysohn型积分算子作用下，用有限个点组成的集合来逼近空间$L_p,$ $p>1,$的闭球的积分漏斗.
英文摘要：
Approximations of the image and integral funnel of the closed ball of the space $L_p,$ $p>1,$ under Urysohn type integral operator are considered. The closed ball of the space $L_p,$ $p>1,$ is replaced by the set consisting of a finite number of piecewise-constant functions and it is proved that in the appropriate specifying of the discretization parameters, the images of defined piecewise-constant functions form an internal approximation of the image of the closed ball. Applying this result, the integral funnel of the closed ball of the space $L_p,$ $p>1,$ under Urysohn type integral operator is approximated by the set consisting of a finite number of points.
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