THE RATE OF CONVERGENCE ON SCHRODINGER OPERATOR

摘要

Recently, Du, Guth and Li showed that the Schro-dinger operator e~(etΔ) satisfies lim_(t→0) e~/(itΔ) f = f almost everywhere for all f ∈ H~S(R~2), provided that s > 1/3. In this paper, we discuss the rate of convergence on e~(it∈)(f) by assuming more regularity on f. At n = 2, our result can be viewed as an application of the Du-Guth-Li theorem. We also address the same issue on the cases n = 1 and n > 2.