A note on unique continuation for Schrödinger’s operator

Kenig, Carlos E.; Sogge, Christopher D.

doi:10.1090/S0002-9939-1988-0943081-3

A note on unique continuation for Schrödinger’s operator
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by Carlos E. Kenig and Christopher D. Sogge PDF

Proc. Amer. Math. Soc. 103 (1988), 543-546 Request permission

Abstract:

In this paper we shall prove a unique continuation theorem for Schrödinger’s operator, $i\partial /\partial t - \Delta$. This will be a consequence of "uniform Sobolev inequalities" for operators which are the Schrödinger operator plus lower order terms in $x$.

References

Lars Hörmander, Uniqueness theorems for second order elliptic differential equations, Comm. Partial Differential Equations 8 (1983), no. 1, 21–64. MR 686819, DOI 10.1080/03605308308820262
David Jerison and Carlos E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. (2) 121 (1985), no. 3, 463–494. With an appendix by E. M. Stein. MR 794370, DOI 10.2307/1971205
C. E. Kenig, A. Ruiz, and C. D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Math. J. 55 (1987), no. 2, 329–347. MR 894584, DOI 10.1215/S0012-7094-87-05518-9
Robert S. Strichartz, A priori estimates for the wave equation and some applications, J. Functional Analysis 5 (1970), 218–235. MR 0257581, DOI 10.1016/0022-1236(70)90027-3
Robert S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), no. 3, 705–714. MR 512086