On the gap property of a linearized NLS operator

2021/10/27 by Li, Dong, Yang, Kai
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2110.14393

Abstract

We consider general non-radial linearization about the ground state to the cubic nonlinear Schrödinger equation in dimension three. We introduce a new compare-and-conquer approach and rigorously prove that the interval (0, 1] does not contain any eigenvalue of L₊ or L_-. The method can be adapted to many other spectral problems.

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