Self-Adjoint Extensions of Differential Operators With Potentials-Point Interactions

Abstract

This paper deals with ordinary differential operators generated in Hilbert space by the differential expression

1[.] = (-1)(n) d(2n)/dx(2n) + (n-1)Sigma(j=0) (-1)(j) d(j)/dx(j) (P-j(x) d(j)/dx(j)),

where P-j (x), j = 0, 1, ...,n 1, is a point interactions of first order, such that integral P-j (xi) d xi is an element of L-2 (a,b), j = 0, 1, ...,n - 1. The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint extensions of the minimal operator are described.