On the Spectral Properties of the Weighted Mean Difference Operator Gu, v;Δ over the Sequence Space ℓ1. (16th June 2014) - Baliarsingh, P.; Dutta, S.
Abstract : In the present work the generalized weighted mean difference operatorG u, v ; Δ has been introduced by combining the generalized weighted mean and difference operator under certain special cases of sequencesu = ( u k ) andv = ( v k ) . For any two sequencesu andv of either constant or strictly decreasing real numbers satisfying certain conditions the difference operatorG u, v ; Δ is defined by( G ( u, v ; Δ ) x ) k = ∑ i = 0 k ‍ u k v i ( x i - x i - 1 ) withx k = 0 for allk < 0 . Furthermore, we compute the spectrum and the fine spectrum of the operatorG u, v ; Δ over the sequence spacel 1 . In fact, we determine the spectrum, the point spectrum, the residual spectrum, and the continuous spectrum of this operator on the sequence spacel 1 .