Representation of higher-order dispersive operators via short-time Fourier transform and its application

Abstract

In this paper, we propose a new representation of the solution to higher-order dispersive equations (which include the free Schrödinger equation and the Airy equation) by using the short-time Fourier transform. As its application, we give $M^{p,q}$-$M^{p,q}_s$, $M^{p,q}$-$M^{p^\prime,q}$ and Strichartz type estimates for the solutions in the framework of the modulation spaces $M^{p,q}_s$.