A General Norm on Extension of a Hilbert’s Type Linear Operator

Abstract

The main purpose of this paper is to study a general norm on extension of a Hilbert’s type linear operator in the continuous and discrete form. In addition to expressing the norm of a Hilbert’s type linear operator T : L 2 (0,∞) → L 2 (0,∞), a more general case with λ > 0, for the continuous form has been studied. By putting λ = 1 a norm of extension of Hilbert’s integral linear operator is obtained. Similar results have been expressed for series when 0 < λ 6 2