Abstract We compute the deficiency spaces of operators form $H_A{\hat {\otimes }} I + I{\hat H_B$ , for symmetric $H_A$ and self-adjoint $H_B$ . This enables us to construct extensions (if they exist) by means von Neumann's theory. The structure this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47 (38) (2014) 385301], but only proven...

We study the exterior derivative as a symmetric unbounded operator on square integrable 1-forms on a 3D bounded domain D. We aim to identify boundary conditions that render this operator self-adjoint. By the symplectic version of the Glazman-Krein-Naimark theorem this amounts to identifying complete Lagrangian subspaces of the trace space of H(curl, D) equipped with a symplectic pairing arising...

In the paper the one-dimensional one-center scattering problem with the initial potential α|x|−1 on the whole axis is treated and reduced to the search for allowable self-adjoint extensions. Using the laws of conservation as necessary conditions in the singular point alongside with account of the analytical structure of fundamental solutions, it allows us to receive exact expressions for the wa...

The classical problem of counting the number real zeros a polynomial was solved long time ago by Sturm. analogous that has on unit circle is, however, still an open problem. In this paper, we show second can be reduced to first one through use suitable pair M\"obius transformations - often called Cayley have property mapping onto line and vice versa. Although method applies arbitrary complex po...

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...