HADAMARD FINITE-PART CONCEPT IN DIMENSION N-GREATER-THAN-OR-EQUAL-TO-2, DISTRIBUTIONAL DEFINITION, REGULARIZATION FORMS AND DISTRIBUTIONAL DERIVATIVES

The aim of this paper is to apply the Hadamard finite part concept to singular pseudo-functions such as a(theta)r(beta) log(j) r, where r2 : = x1(2) + ... + x(n)2 in R(n), j is-an-element-of N, beta less-than-or -equal-to -n, and a is a function depending on theta := OM/r. For thes e specific pseudo-functions both regularizations forms and distributio nal derivatives, [GRAPHICS] where p,p1,...,p(n) are positive integers with p = p1 + ... + p(n), are investigated. Whenever possible the resu lts are compared with those obtained by Estrada & Kanwal (1985, 1989).