On a Weyl-Titchmarsh Theory for Discrete Symplectic Systems on a Half Line
Recently, Bohner and Sun  introduced basic elements of a Weyl–Titchmarsh theory into the study of discrete symplectic systems. We extend this development through the introduction of Weyl–Titchmarsh functions together with a preliminary study of their properties. A limit point criterion is described and characterized. Green’s function for the half-line is introduced as a limit of such functions in the regular case and half-line solutions obtained are seen to satisfy λ-dependent boundary conditions at infinity.
S. L. Clark and P. Zemánek, "On a Weyl-Titchmarsh Theory for Discrete Symplectic Systems on a Half Line," Applied Mathematics and Computation, Elsevier, Jan 2010.
The definitive version is available at http://dx.doi.org/10.1016/j.amc.2010.08.029
Mathematics and Statistics
Keywords and Phrases
discrete symplectic system; Weyl-Titchmarsh M-function; regular spectral problem; singular spectral problem; Riccati equation; limit point case; limit circle case; Green's function
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