On the compactness of the resolvent of a Schrodinger type singular operator with a negative parameter

In this paper, we consider a Schrodinger-type operator with a negative parameter and a complex potential L-t = -Delta + (-t(2) + itb(x) + q(x)), x is an element of R-n, n >= 1, i(2)= -1, where t is a parameter that arises when studying hyperbolic operators in the space L-2 (Rn+1). We assume with respect to the coefficients of the operator L-t that they are continuous in R-n strongly growing and rapidly oscillating functions at infinity and satisfy the condition vertical bar b(x)vertical bar >= delta(0) > 0, q(x) >= delta > 0. In the paper, under these assumptions, it is proved that there exists a bounded inverse operator for all t is an element of R and found a condition that ensures the compactness of the resolvent. Note that in the paper we construct regularizing operator, i.e. the question of the existence of a resolvent of an operator with singular coefficients reduces to the case of operators with smooth periodic coefficients. (C) 2021 Elsevier Ltd. All rights reserved.