A study on a class of generalized Schrodinger operators

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.

Automated summary

This paper discusses the pointwise convergence and convergence rate along curves for a class of generalized Schrodinger operators, showing the validity of almost sharp results under small perturbations and obtaining specific applications. The relationship between smoothness of functions and convergence rate, as well as the convergence rate based on growth conditions and regularity, are established for a wide class of operators. Additionally, pointwise convergence results and convergence rates for generalized Schrodinger operators with non-homogeneous phase functions are obtained.