Uniqueness problem for accretive Schrödinger operators with complex singular coefficients

Abstract This paper studies the uniqueness problem for the one‐dimensional Schrödinger operator associated with the formal differential expression in the complex Hilbert space . The coefficients of the expression are complex‐valued and satisfy where the derivative is understood in the sense of distributions. In particular, the potential can be a Radon measure on the line. With the help of specially selected quasi‐derivatives, the expression is treated as a quasi‐differential expression. The domains of the minimal and maximal operators associated with the expression in the space are described. We find constructive conditions on the behaviour of near that guarantee that if the operator is accretive. We prove that these conditions are sharp even in the class of differential operators with smooth real‐valued coefficients. Examples are given to illustrate the main results of the paper.