In this paper, we consider the pointwise convergence for a class of generalized Schrodinger operators with suitable perturbations, and convergence rate along curves for a class of generalized Schrodinger operators with polynomial growth. We show that the almost sharp results of pointwise convergence remain valid for a class of generalized Schrodinger operators under small perturbations. As applications, we get the almost sharp pointwise convergence results for Boussinesq operator and Beam operator in R-2. Moreover, the pointwise convergence results for a class of non-elliptic Schrodinger operators with finite-type perturbations are obtained. Furthermore, we build the relationship between smoothness of the functions and convergence rate along curves for a class of generalized Schrodinger 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, pointwise convergence results along curves for a class of generalized Schrodinger operators with non-homogeneous phase functions are obtained and then the convergence rate is established. (C) 2021 Elsevier Inc. All rights reserved.
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