Pointwise Convergence Along Restricted Directions for the Fractional Schrodinger Equation

We consider the pointwise convergence problem for the solution of Schrodinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson's problem as the simplest case and was studied in general by Cho et al. We extend their result from the case of the classical Schrodinger equation to a class of equations which includes the fractional Schrodinger equations. To achieve this, we significantly simplify their proof by completely avoiding a time localization argument.