2014/03/16 by Vadim Mogilevskii, Mogilevskii, Vadim · 1 citation
Computer Science · Materials Science · Mathematics · #34B08 #34B40 #47A06 #47B25 #FOS: Mathematics #Functional Analysis (math.FA) #Magnetism in coordination complexes #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #math.FA #msc:34B08 #msc:34B40 #msc:47A06 #msc:47B25
paper · pdf · doi:10.48550/arxiv.1403.3955
arXiv admin note: text overlap with arXiv:1307.6741
arxiv created 2014/03/16 · openalex publication_date 2014/03/16 · arxiv updated 2014/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study general (not necessarily Hamiltonian) first-order symmetric system J y'-B(t)y=\D(t) f(t) on an interval \cI=[a,b) with the regular endpoint a and singular endpoint b. It is assumed that the deficiency indices n_±(\Tmi) of the corresponding minimal relation \Tmi in \LI satisfy n-(\Tmi)≤ n+(\Tmi). We describe all generalized resolvents y=R(ł)f, f∈\LI, of \Tmi in terms of boundary problems with ł-depending boundary conditions imposed on regular and singular boundary values of a function y at the endpoints a and b respectively. We also parametrize all characteristic matrices \Om(ł) of the system immediately in terms of boundary conditions. Such a parametrization is given both by the block representation of \Om(ł) and by the formula similar to the well-known Krein formula for resolvents. These results develop the uStraus' results on generalized resolvents and characteristic matrices of differential operators.