Spectral enclosures for non-self-adjoint discrete Schrödinger operators

2019/03/20 by Ibrogimov, Orif O., Štampach, František
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1903.08620

Abstract

We study location of eigenvalues of one-dimensional discrete Schrödinger operators with complex ℓ^p-potentials for 1≤ p≤ ∞. In the case of ℓ¹-potentials, the derived bound is shown to be optimal. For p>1, two different spectral bounds are obtained. The method relies on the Birman-Schwinger principle and various techniques for estimations of the norm of the Birman-Schwinger operator.

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