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In this study, we are concerned with introducing Weyl-Titchmarsh theory for aclass of dynamic linear Hamiltonian nabla systems over a half-line on Sturmiantime scales. After developing fundamental properties of solutions and regularspectral problems, we introduce the corresponding maximal and minimal operatorsfor the system. Matrix disks are constructed and proved to be nested andconverge to a limiting set. Some precise relationships among the rank of thematrix radius of the limiting set, the number of linearly independent squaresummable solutions, and the defect indices of the minimal operator areestablished. Using the above results, a classification of singular dynamiclinear Hamiltonian nabla systems is given in terms of the defect indices of theminimal operator, and several equivalent conditions on the cases of limit pointand limit circle are obtained, respectively. These results unify and extendcertain classic and recent results on the subject in the continuous anddiscrete cases, respectively, to Sturmian time scales.

Unifying discrete and continuous Weyl-Titchmarsh theory via a class of linear Hamiltonian systems on Sturmian time scales