International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 749-754
On defining the generalized functions and
Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Canada
Received 20 April 1992; Revised 10 August 1992
Copyright © 1993 E. K. Koh and C. K. Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In a previous paper (see ), we applied a fixed -sequence and neutrix limit due to Van
der Corput to give meaning to distributions and for and . In this paper,
we choose a fixed analytic branch such that is an analytic single-valued function and
define on a suitable function space . We show that . Similar results on are
obtained. Finally, we use the Hilbert integral where , to redefine
as a boundary value of . The definition of is independent of the choice of -sequence.