Schrödinger Pointwise Convergence Problem

The Schrödinger pointwise convergence problem asks how much Sobolev space regularity of an initial function guarantees that its free Schrödinger equation evolution returns to almost everywhere as time tends to zero. With , a Gaussian-regularized evolution is

where . The unregularized evolution is obtained by taking the limit as tends to zero before asking about convergence as time tends to zero. The regularity space uses the Bessel potential space norm with .