Schr\"odinger ultrahyperbolic equations with singular coefficients

In this paper we investigate the Cauchy problem for Schr\"odinger 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.