On the Deficiency Indices of Block Jacobi Matrices Related to Dirac Operators with Point Interactions

Abstract

The paper concerns with infinite block Jacobi matrices J with p × p-matrix entries. We present new conditions for these block matrices to be selfadjoint and have discrete spectrum. In our previous papers there was established a close relation between a class of such matrices and 2p × 2p Dirac operators with point interactions in L 2 (R; C 2p). For block Jacobi matrices J of this class we present several conditions ensuring either maximality or intermediatory of their deficiency indices. Applications to Dirac and matrix Schrodinger operators are given. It is worth mentioning that the above mentioned connection is employed here in both directions for the first time. In particular, the property of J to have maximal deficiency indices was firstly established for Dirac operators.

On the calculation of the discrete spectra of one‐dimensional Dirac operators

“…The spectral properties of the Dirac operators with singular potential have been intensively studied in connection with their physical applications and as an object of application of new methods of the spectral theory of unbounded operators. We refer to the following papers [20][21][22][23][24][25][26][27][28][29][30][31][32] and the literature therein cited, in which conditions for self-adjointness, and the location of the discrete and essential spectra were obtained.…”