Bounds on eigenvalues of perturbed Lam\'e operators with complex potentials

DOI10.3934/MINE.2022037arXiv1904.08445MaRDI QIDQ6317387

Lucrezia Cossetti

Publication date: 17 April 2019

Abstract: Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. This paper provides some improvement in the state of the art in this topic. Precisely, we address the question of finding quantitative bounds on the discrete spectrum of the perturbed Lam'e operator of elasticity $-Delt{a}^{a}st+V$ in terms of $L^p$-norms of the potential. Original results within the self-adjoint framework are provided too.

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

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