Spectra and fine spectra of the generalized upper difference operator with triple repetition Δ3ab$\begin{array}{}\displaystyle\Delta_{3}^{ab}\end{array}$ on the Hahn sequence space

Abstract

Abstract The goal of this paper is to obtain the spectra and fine spectra of the matrix Δ 3 a b $\begin{array}{}\displaystyle\Delta_{3}^{ab}\end{array}$ on the Hahn space. Also, we explore some ideas of how to study the problem for a general form of the matrix, namely, the matrix Δ n a b $\begin{array}{}\displaystyle\Delta _{n}^{ab}\end{array}$ where the non-zero diagonals are the entries of a n-ary repetition sequence.