Approximation of the Image of the Hilbert-Schmidt Integral Operator

Abstract

In this paper an approximation of the image of the closed ball of the space $L_p$ $(p>1)$ centered at the origin with radius $r$ under Hilbert-Schmidt integral operator $F(\cdot ):L_p\to L_q$ $\left(\frac{1}{p}+\frac{1}{q}=1\right)$ is presented. An error estimation for given approximation is obtained.