On the compactness of the resolvent of a Schrödinger type singular operator with a negative parameter
Muratbekov M.B. Muratbekov M.M.
October 2021Elsevier Ltd
Chaos, Solitons and Fractals
2021#151
In this paper, we consider a Schrödinger-type operator with a negative parameter and a complex potential Lt=−Δ+(−t2+itb(x)+q(x)),x∈Rn,n≥1,i2=−1, where t is a parameter that arises when studying hyperbolic operators in the space L2(Rn+1). We assume with respect to the coefficients of the operator Lt that they are continuous in Rn strongly growing and rapidly oscillating functions at infinity and satisfy the condition |b(x)|≥δ0>0,q(x)≥δ>0. In the paper, under these assumptions, it is proved that there exists a bounded inverse operator for all t∈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.
Coercive estimates , Compactness of the resolvent , Hyperbolic type , Negative parameter , Schrödinger operator , Singular differential operator
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Taraz Regional University named after M.Kh.Dulaty, Suleymenov str. 7, Taraz, Kazakhstan
Kazakh University of Economics, Finance and International Trade, Zhubanov str. 7, Astana, Kazakhstan
Taraz Regional University named after M.Kh.Dulaty
Kazakh University of Economics
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