IJPAM: Volume 25, No. 1 (2005)

BEST APPROXIMATION IN A HILBERT SPACE

E. Aghdassi$^1$, S.F. Rzaev$^2$
$^{1,2}$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 the shift operator on Hilbert spaces and by using this operator we define the modulus of continuity of fractional index, including relation to the $K$-functional and we prove the fractional analog we direct and inverse theorems of approximation theory.

Received: August 10, 2005

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: 2005
Volume: 25
Issue: 1