Absence of eigenvalues of non-self-adjoint Robin Laplacians on the half-space

被引：8

作者：

Cossetti, L. ^{[1
,2
]}

Krejcirik, D. ^{[1
]}

机构：

[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Math, Trojanova 13, Prague 12000 2, Czech Republic

[2] Karlsruhe Inst Technol, Inst Anal, Dept Math, Englerstr 2, D-76131 Karlsruhe, Germany

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2020年 / 121卷 / 03期

关键词：

35J05 (primary); 35P15; 47A10; 81Q12 (secondary); SCHRODINGER-OPERATORS; HELMHOLTZ-EQUATION; EXTENSION PROBLEM; SCATTERING; THEOREM; BOUNDS;

D O I：

10.1112/plms.12327

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By developing the method of multipliers, we establish sufficient conditions which guarantee the total absence of eigenvalues of the Laplacian in the half-space, subject to variable complex Robin boundary conditions. As a further application of this technique, uniform resolvent estimates are derived under the same assumptions on the potential. Some of the results are new even in the self-adjoint setting, where we obtain quantum-mechanically natural conditions.

引用

页码：584 / 616

页数：33

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