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Friedrichs extensions for a class of singular discrete linear Hamiltonian systems

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arxiv 2311.08665 v1 pith:CZXFEWRQ submitted 2023-11-15 math.SP

classification math.SP
keywords friedrichsconditionsextensionlinearrecessivesolutionsboundaryclass
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This paper is concerned with the characterizations of the Friedrichs extension for a class of singular discrete linear Hamiltonian systems. The existence of recessive solutions and the existence of the Friedrichs extension are proved under some conditions. The self-adjoint boundary conditions are obtained by applying the recessive solutions and then the characterization of the Friedrichs extension is obtained in terms of boundary conditions via linear independently recessive solutions.

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  1. The Friedrichs extension of a class of discrete symplectic systems

    math.SP 2024-12 conditional novelty 6.0 of 10

    The Friedrichs extension of a lower semibounded minimal linear relation from a discrete symplectic system is exactly the maximal relation whose elements vanish at zero and are limit-orthogonal to the columns of a rece...

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