| Full text | |
| Author(s): |
Menegatto, V. A.
;
Oliveira, C. P.
;
Peron, A. P.
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF APPLIED ANALYSIS; v. 15, n. 1, p. 17-pg., 2009-06-01. |
| Abstract | |
We analyze term-by-term differentiability of uniformly convergent series of the form Sigma(infinity)(k=0) rho Y-k(k)(x)<(Y-k(y))over bar>, x, y is an element of Sm-1,where Sm-1 is the unit sphere in R-m, rho(k) >= 0,k - 0, 1, . . . , Sigma(infinity)(k=0) rho(k) > 0,and {Y-k} is a sequence of spherical harmonics or even more general functions. Since this class of kernels includes the continuous positive de fi nite kernels on Sm-1, the results in this paper will show that, under certain conditions, the action of convenient differential operators on positive de fi nite (strictly positive de fi nite) kernels on Sm-1 generate positive de fi nite kernels. (AU) | |