Pointwise convergence of solutions to the nonelliptic Schrodinger equation

It is conjectured that the solution to the Schrodinger equation in Rn+1 converges almost everywhere to its initial datum f, for all f is an element of H-s(R-n), if and only if s >= (1)/(4). It is known that there is an s < (1)/(2) for which the solution converges for all f is an element of H-s (R-2). We show that the solution to the nonelliptic Schrodinger equation, i partial derivative(t)u + (partial derivative(2)(x) - partial derivative(2)(y))u = 0, converges to its initial datum f, for all f is an element of H-s(R-2), if and only if s >= (1)/(2). Thus the pointwise behaviour is worse than that of the standard Schrodinger equation. In higher dimensions, we have similar results with the loss of the endpoint.