2015/07/19 by Yu. M. Arlinskiĭ, Arlinskiĭ, Yu. M., Андрей Борисович Попов +1
Computer Science · Mathematics · #47A06 #47A07 #47A20 #47B25 #47B44 #82B23 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1507.05327
openalex publication_date 2015/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our article [15] description in terms of abstract boundary conditions of all m-accretive extensions and their resolvents of a closed densely defined sectorial operator S have been obtained. In particular, if \H,Γ\ is a boundary pair of S, then there is a bijective correspondence between all m-accretive extensions S of S and all pairs ⟨ Z,X⟩, where Z is a m-accretive linear relation in H and X:dom(Z)→ran(SF) is a linear operator such that: ‖Xe‖2\leqslantRe(Z(e),e)H ∀ e\indom(Z). As is well known the operator S admits at least one m-sectorial extension, the Friedrichs extension. In this paper, assuming that S has non-unique m-sectorial extension, we established additional conditions on a pair ⟨ Z,X⟩ guaranteeing that corresponding S is m-sectorial extension of S. As an application, all m-sectorial extensions of a nonnegative symmetric operator in a planar model of two point interactions are described.