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(a_{0},a_{2},…,a_{n-1};0;b_{0},b_{1},…,b_{n-1})) where the non-zero diagonals are the entries of an oscillatory sequence
