Approximation of Hypersingular Integral Operators With Cauchy Kernel

ABSTRACT

In the present article, the hypersingular integral operator with Cauchy kernel H is approximated by a sequence of operators of a special form, and it is proved that the approximating operators H_n strongly converge to the operator H and for an algebraic polynomial of degree not higher than n the operators H_n and H coincide. Therefore, the estimate established in this article yields more exact results in terms of the convergence rate than traditional methods. At the end we give the approximate solution of the hypersingular integral equation of the first kind.

KEYWORDS:

• Best mean-square approximation
• Cauchy kernel
• hypersingular integral equation
• hypersingular integral operator

MATHEMATICS SUBJECT CLASSIFICATION:

• 41A35
• 47A58
• 65R20
• 45E05