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 recessive solution.
Friedrichs extensions for a class of singular discrete linear Hamiltonian systems
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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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The Friedrichs extension of a class of discrete symplectic systems
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 recessive solution.