Schrödinger ultrahyperbolic equations with singular coefficients

Abstract

In this paper we investigate the Cauchy problem for Schrödinger ultrahyperbolic equations with singular (less than continuous) coefficients. We prove $H^{\infty }$ well-posedness in the very weak sense under suitable assumptions of the distributional structure of the coefficients and decay on the lower order terms. Consistency is proven with the classical $H^{\infty }$-results when the equation coefficients are smooth.