Existence of a spectral measure for second-order delta dynamic equations on semi-infinite time scale intervals

► We prove existence of a spectral measure for second-order delta dynamic equations on time scales. ► The result implies, in particular, existence of an orthogonality measure in the discrete case. ► An expansion in eigenfunctions formula is established in terms of the spectral measure. ► The result extends the well-known results to the more general context of time scales.