2023/07/29 by Muhamed Borogovac, Borogovac, Muhamed
Engineering · #(2020): 46C20 47B50 47B25 47A06 34B20 #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in engineering #Railway Engineering and Dynamics #Tribology and Wear Analysis
paper · pdf · doi:10.48550/arxiv.2307.15954
openalex publication_date 2023/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given Krein and Hilbert spaces ( K,[.,.] ) and ( H, ( .,. ) ), respectively, the concept of the boundary triple Π=(H, Γ0, Γ1) is generalized through the abstract Green's identity for the isometric relation Γ between Krein spaces ( K2, [ .,.]K2 ) and (H2, [ .,.]H2 ) without any conditions on \dom Γ and \ran Γ. This also means that we do not assume the existence of a closed symmetric linear relation S such that \dom Γ=S+, which is a standard assumptions in all previous research of boundary triples. The main properties of such a general Green's boundary model are proven. In the process, some useful properties of the isometric relation V between two Krein spaces X and Y are proven. Additionally, surprising properties of the unitary relation Γ: K2 \rightarrowH2 and the self-adjoint main transformation A of Γ are discovered. Then, two statements about generalized Nevanlinna families are generalized using this Green's boundary model. Furthermore, several previously known boundary triples involving a Hilbert space K and reduction operator Γ: K2 \rightarrowH2, such as AB-generalized, B-generalized, ordinary, isometric, unitary, quasi-boundary, and S-generalized boundary triples, have been extended to a Krein space K and linear relation Γ using the Green's boundary model approach.