The purpose of this paper is to define and study the spaces [ĉ,M, p](∆u , q, s), [ĉ,M, p, ] θ 0(∆ m u , q, s) and [ĉ,M, p, ] θ ∞(∆ m u , q, s) of lacunary convergent sequences. We also study some inclusion relations between these spaces and some properties and theorems. 2000 Mathematics Subject Classification:40D05, 40A05. 1.Introduction and definitions Let w denote the set of all complex seque...

We find asymptotics of entries Jacobi matrices with lacunary spectral data under some additional growth conditions. also prove the inverse results. In addition, we study connections between matrices, canonical systems and de Branges spaces for data.

Using the concept of Orlicz function and uncertainty theory, some new class lacunary convergent sequences defined by functions have been introduced with convergence concepts in this paper. Some topological properties sequence spaces along inclusion relations investigated.