IJPAM: Volume 31, No. 1 (2006)

SPLINE GENERALIZED SPHERICAL FUNCTIONS
ON THE SPHERE

E. Aghdassi$^1$, S.F. Rzaev$^2$
$^{1,2}$Department of Applied Mathematics
Faculty of Mathematical Sciences
University of Tabriz
Tabriz, IRAN
$^1$e-mail: esaghdassi@tabrizu.ac.ir
$^2$e-mail: rzseymur@hotmail.com


Abstract.In this paper we consider periodical functions defined on

\begin{displaymath}\sigma=(0\leq \phi_1 \leq 2\pi; 0\leq \theta \leq \pi, 0\leq \phi_2 \leq 2\pi)\end{displaymath}

in $L_2(\sigma)$ Hilbert space quipped with spacial scalar product and corresponding norm. In space $W_2^r(B,\sigma)$ the convex programming problem which is called Favard problem is studied where $B$ is a prescribed operator.

Received: May 20, 2006

AMS Subject Classification: 42C10, 43A77, 43A90

Key Words and Phrases: Hilbert space, self-adjoint operator, $k$-functional

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 1