Abstract
Let S be a closed linear relation with equal defect numbers n ≤ ∞ in a Hilbert space. We prove that for each n-dimensional subspaceL of generalized elements, S has anL-resolvent matrix, and we give the characteristic properties of suchL-resolvent matrices. The results are illustrated at the example of a regular canonical differential relation, and it is shown that its generalized resolvents are given by certain boundary problems, containing the eigenvalue parameter in the boundary condition.
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Langer, H., Textorius, B. L-resolvent matrices of symmetric linear relations with equal defect numbers; applications to canonical differential relations. Integr equ oper theory 5, 208–243 (1982). https://doi.org/10.1007/BF01694040
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DOI: https://doi.org/10.1007/BF01694040