Uniform resolvent estimates and absence of eigenvalues for Lame operators with complex potentials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Cossetti, Lucrezia¹ 

[1] Sapienza Univ Roma, Dipartimento Matemat, Ple A Moro 5, I-00185 Rome, Italy

关键词: Lame operator;    Helmholtz equation;    Spectral Theory;    Resolvent estimates;   

DOI  :  10.1016/j.jmaa.2017.05.053

来源: Elsevier

【 摘 要 】

We consider the 0-order perturbed Lame operator -Delta* + V(x). It is well known that if one considers the free case, namely V = 0, the spectrum of -Delta* is purely continuous and coincides with the non-negative semi-axis. The first purpose of the paper is to show that, at least in part, this spectral property is preserved in the perturbed setting. Precisely, developing a suitable multipliers technique, we will prove the absence of point spectrum for Lame operator with potentials which satisfy a variational inequality with suitable small constant. We stress that our result also covers complex-valued perturbation terms. Moreover the techniques used to prove the absence of eigenvalues enable us to provide uniform resolvent estimates for the perturbed operator under the same assumptions about V. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free