Let G denote the Grushin operator on Rⁿ⁺¹. It is well known that the Grushin-Schrodinger equation is totally non-dispersive and hence the classical approach to obtain Strichartz estimates fails. In this paper, we prove a restriction theorem with respect to the scaled Hermite-Fourier transform on Rⁿ⁺² for certain surfaces in N₀ⁿ x R* x R and as an application, we obtain anisotropic Strichartz estimates for the Grushin-Schrodinger equation and for the Grushin wave equation.

The authors would like to thank the referee for careful reading and fruitful comments towards the improvement of the manuscript. The first author wishes to thank the Ministry of Human Resource Development, India for the research fellowship and Indian Institute of Technology Guwahati, India for the support provided during the period of this work.