Convergence problems along curves for generalized Schr\"{o}dinger operators with polynomial growth

Abstract

In this paper we build the relationship between smoothness of the functions and convergence rate along curves for a class of generalized Schr\"{o}dinger operators with polynomial growth. We show that the convergence rate depends only on the growth condition of the phase function and regularity of the curve. Our result can be applied to a wide class of operators. In particular, convergence results along curves for a class of generalized Schr\"{o}dinger operators with non-homogeneous phase functions is built and then the convergence rate is established.