HADAMARDS FINITE-PART CONCEPT IN DIMENSION N-GREATER-THAN-OR-EQUAL-TO-2 - DEFINITION AND CHANGE OF VARIABLES, ASSOCIATED FUBINIS THEOREM, DERIVATION

Some usual and important operations: change of variables, application of Fubini's theorem and derivation with respect to the isolated singul arity (in the present work with respect to the origin of the spherical coordinates (tau, theta)) are studied for the following singular inte gral I-alpha,I-j(a):=fp integral(Omega U)a(theta)tau(a)log(j) tau dx, where alpha is an element of C, Re(alpha) less than or equal to -n, j is an element of N, a is an element of L-1(Sigma(n),C) and the symbol fp integral(Omega,U) means an integration on the set Omega in the fini te part sense of Hadamard with respect to the domain configuration U. Moreover, applications to integral operators are outlined.