On a Weyl-Titchmarsh theory for discrete symplectic systems on a half line

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Authors	CLARK Stephen L ZEMÁNEK Petr
Year of publication	2010
Type	Article in Periodical
Magazine / Source	Applied Mathematics and Computation
MU Faculty or unit	Faculty of Science
Citation
web	http://dx.doi.org/10.1016/j.amc.2010.08.029
Field	General mathematics
Keywords	Discrete symplectic system; Weyl-Titchmarsh M-function; Regular spectral problem; Singular spectral problem; Riccati equation; Limit point case; Limit circle case; Green's function.
Attached files	On_a_WeylOTitchmarsh_theory_for_discrete_symplectic_systems_on_a_half_line__Clark___Zemanek_.pdf
Description	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 lambda-dependent boundary conditions at infinity.
Related projects:	Oscillation and spectral theory of differential and difference systems Matematické struktury