A Sturm–Liouville Theory for Hahn Difference Operator

Spectral Theory of Singular Hahn Difference Equation of the Sturm-Liouville Type

“…then we deduce that the problem given by (3), (4) and (5) is a regular problem. In [10], Annaby et al showed that the boundary value problem (3) with the boundary conditions (4) and (5) has a compact resolvent, thus this problem has a purely discrete spectrum.…”

“…which is called the Parseval equality (see [10]). Now we will introduce the nondecreasing step function q −n on [0, ∞) by…”

Spectral analysis of Hahn-Dirac system

“…In this section, we recall some necessary concepts of the Hahn calculus. For more details, the reader may want to consult [6], [9], [10], [7]. Throughout the paper, we let q 2 (0; 1) and !…”

“…Sitthiwirattham [22] considers the nonlocal boundary value problem for the nonlinear Hahn difference equation. Recently, in [7], the regular Hahn-Sturm-Liouville problem…”

The spectral expansion for the Hahn–Dirac system on the whole line

“…Sitthiwirattham [26] investigated the nonlocal boundary value problem for nonlinear Hahn difference equations. Recently, in [9], the regular Hahn-Sturm-Liouville problem was studied. Annaby et al [9] defined a Hilbert space of ω, q -square summable functions.…”