On powers of the Heaviside function for negative integers

The distributions (xr+ )−s and (xr+ )−s − were defined as the neutrix limit of the sequences ((xr+ )−s )n and ((xr+ )−s − )n respectively for r, s = 1, 2, . . . , see [J.D. Nicholos, B. Fisher, The distribution composition (xr+ )−s , J. Math. Anal. Appl. 258 (2001) 131–145; B. Fisher, On defining the distribution (xr+ )−s − , Univ. u Novom Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 15 (1985) 119–129].We here consider these distributions when r = 0. In other words, we define the sth powers of the Heaviside function H(x) in the distributional sense for negative integers. Further compositions are also considered. © 2006 Elsevier Inc. All rights reserved