Arkiv för Matematik

, Volume 28, Issue 1–2, pp 159–182 | Cite as

A unique continuation theorem for second order parabolic differential operators

  • C. D. Sogge


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Carleson, L. andSjölin, P., Oscillatory integrals and a multiplier problem for the disc,Studia Math. 44 (1972), 287–299.MATHMathSciNetGoogle Scholar
  2. 2.
    Fefferman, C., A note on spherical summation multipliers,Israel J. Math. 15 (1973), 44–52.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Garofalo, N. andKenig, C. E.,Personal communication.Google Scholar
  4. 4.
    Hörmander, L., The spectral function of an elliptic operator,Acta Math. 88 (1968), 193–218.CrossRefGoogle Scholar
  5. 5.
    Hörmander, L., “The analysis of linear partial differential operators”,Vol. I, Springer-Verlag, New York, Berlin, 1983.Google Scholar
  6. 6.
    Kenig, C. E. andSogge, C. D., A note on unique continuation for Schrödinger's operator,Proc. Amer. Math. Soc. 103 (1988), 543–546.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Nirenberg, L., Uniqueness in Cauchy problems for differential equations with constant leading coefficients,Comm. Pure Appl. Math. 10 (1957), 89–105.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Saut J. C. andScheurer, B., Unique continuation for some evolution equations,J. Diff. Equations 66 (1987), 118–139.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Seeger, A., On quasiradial Fourier multipliers and their maximal functions,J. reine ang. Math. 370 (1986), 61–73.MATHMathSciNetGoogle Scholar
  10. 10.
    Sogge, C. D., Oscillatory integrals and unique continuation for second order elliptic differential equations,J. Amer. Math. Soc. 2 (1989), 491–515.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Stein, E. M., Oscillatory integrals in Fourier analysis, in “Beijing lectures in harmonic analysis”, Princeton Univ. Press, Princeton, NJ, 1986, pp. 307–356.Google Scholar
  12. 12.
    Strichartz, R., Restriction of Fourier transform to quadratic surface,Duke Math. J. 44 (1977), 705–714.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Trèves, F., “Introduction to pseudo-differential and Fourier integral operators”,Vol. II, Plenum Press, New York, 1982.Google Scholar
  14. 14.
    Trèves, F., Solution of Cauchy problems modulo flat problems,Comm. Partial Differential Equations 1 (1976), 45–72.CrossRefMathSciNetGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1990

Authors and Affiliations

  • C. D. Sogge
    • 1
  1. 1.UCLALos AngelesUSA

Personalised recommendations