Pseudomodes for biharmonic operators with complex potentials

TL;DR

This paper develops a new WKB-based method to construct pseudomodes for one-dimensional biharmonic operators with complex potentials, revealing the pseudospectrum's shape near infinity and extending applicability to diverse potentials.

Contribution

It introduces a systematic approach that surpasses standard semi-classical methods, enabling analysis of a broad class of complex potentials for biharmonic operators.

Findings

Pseudomodes constructed for complex potentials using WKB method

Description of pseudospectrum shape near infinity

Applicable to potentials from logarithmic to superexponential

Abstract

This article is devoted to the construction of pseudomodes of one-dimensional biharmonic operators with the complex-valued potentials via the WKB method. As a by-product, the shape of pseudospectrum near infinity can be described. This is a newly discovered systematic method that goes beyond the standard semi-classical setting which is a direct consequence. This approach can cover a wide class of previously inaccessible potentials, from logarithmic to superexponential ones.