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On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems
Journal article   Peer reviewed

On M-functions and operator theory for non-self-adjoint discrete Hamiltonian systems

Shatha Jameel Monaquel and Karl Michael Schmidt
Journal of computational and applied mathematics, Vol.208(1), pp.82-101
01/11/2007
DOI: https://doi.org/10.1016/j.cam.2006.10.043

Abstract

Difference operators Discrete Hamiltonian systems Non-self-adjoint operators Weyl-Titchmarsh M-function
We study discrete, generally non-self-adjoint Hamiltonian systems, defining Weyl–Sims sets, which replace the classical Weyl circles, and a matrix-valued M-function on suitable cone-shaped domains in the complex plane. Furthermore, we characterise realisations of the corresponding differential operator and its adjoint, and construct their resolvents.

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