NOTE ON SPECTRUM OF LINEAR DIFFERENTIAL OPERATORS WITH PERIODIC COEFFICIENTS

Abstract

In this paper, by rigorous calculations, we consider L2(R)-spectrum of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that L2(R)-spectrum of the linear operator is determined by the eigenvalues of Floquet matrix.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.