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A note on unique continuation for Schrödinger's operator

Authors: Carlos E. Kenig and Christopher D. Sogge
Journal: Proc. Amer. Math. Soc. 103 (1988), 543-546
MSC: Primary 35J10; Secondary 35B45
MathSciNet review: 943081
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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 [Enhancements On Off] (What's this?)

  • [1] L. Hörmander, Uniqueness theorems for second-order elliptic differential operators, Comm. Partial Differential Equations 8 (1983), 21-64. MR 686819 (85c:35018)
  • [2] D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. 121 (1985), 463-494. MR 794370 (87a:35058)
  • [3] C. E. Kenig, A. Ruiz, and C. D. Sogge, Uniform Sobolev inequalities and unique continuation theorems for second-order constant coefficient differential operators, Duke Math. J. 55 (1987), 329-347. MR 894584 (88d:35037)
  • [4] R. S. Strichartz, A priori estimates for the wave equation and some applications, J. Funct. Anal. 5 (1970), 218-235. MR 0257581 (41:2231)
  • [5] -, Restrictions of Fourier transforms to quadratic surfaces, Duke Math. J. 44 (1977), 705-714. MR 0512086 (58:23577)

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Keywords: Sobolev inequalities, unique continuation, restriction theorems
Article copyright: © Copyright 1988 American Mathematical Society

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