Duke Mathematical Journal

Oscillatory integrals with singular symbols

V. Guillemin and G. Uhlmann

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Article information

Source
Duke Math. J. Volume 48, Number 1 (1981), 251-267.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077314493

Mathematical Reviews number (MathSciNet)
MR610185

Zentralblatt MATH identifier
0462.58030

Digital Object Identifier
doi:10.1215/S0012-7094-81-04814-6

Subjects
Primary: 58G15
Secondary: 35S05: Pseudodifferential operators

Citation

Guillemin, V.; Uhlmann, G. Oscillatory integrals with singular symbols. Duke Mathematical Journal 48 (1981), no. 1, 251--267. doi:10.1215/S0012-7094-81-04814-6. http://projecteuclid.org/euclid.dmj/1077314493.


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References

  • [1] J. J. Duistermaat, Fourier integral operators, Courant Institute of Mathematical Sciences New York University, New York, 1973.
  • [2] J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), no. 3-4, 183–269.
  • [3] V. Guillemin, Singular symbols, manuscript.
  • [4] V. Guillemin and S. Sternberg, Geometric asymptotics, American Mathematical Society, Providence, R.I., 1977.
  • [5] V. Guillemin and S. Sternberg, Some problems in integral geometry and some related problems in microlocal analysis, Amer. J. Math. 101 (1979), no. 4, 915–955.
  • [6] L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183.
  • [7] R. B. Melrose and G. A. Uhlmann, Lagrangian intersection and the Cauchy problem, Comm. Pure Appl. Math. 32 (1979), no. 4, 483–519.
  • [8] R. B. Melrose and G. A. Uhlmann, Microlocal structure of involutive conical refraction, Duke Math. J. 46 (1979), no. 3, 571–582.
  • [9] G. A. Uhlmann, Parametrices for operators with multiple involutive characteristics, Comm. Partial Differential Equations 4 (1979), no. 7, 739–767.