Spectra and fine spectra of the upper triangular band matrix U(a;0;b) on the Hahn sequence space

Abstract

The aim of this paper is to obtain the spectra and fine spectra of the matrix $U(a;0;b)$ 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 $U(a₀,a₁,…,a_{n-1};0;b₀,b₁,…,b_{n-1})$ where the non-zero diagonals are the entries of an oscillatory sequence.