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Transactions of the American Mathematical Society

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ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The FBI transform on compact ${\mathcal {C}^\infty }$ manifolds
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by Jared Wunsch and Maciej Zworski PDF
Trans. Amer. Math. Soc. 353 (2001), 1151-1167 Request permission

Abstract:

We present a geometric theory of the Fourier-Bros-Iagolnitzer transform on a compact ${\mathcal {C}^\infty }$ manifold $M$. The FBI transform is a generalization of the classical notion of the wave-packet transform. We discuss the mapping properties of the FBI transform and its relationship to the calculus of pseudodifferential operators on $M$. We also describe the microlocal properties of its range in terms of the ‚Äúscattering calculus‚ÄĚ of pseudodifferential operators on the noncompact manifold $T^* M$.
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Additional Information
  • Jared Wunsch
  • Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
  • Address at time of publication: Department of Mathematics, SUNY at Stony Brook, Stony Brook, New York 11794-3651
  • Email: jwunsch@math.sunysb.edu
  • Maciej Zworski
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 227055
  • Email: zworski@math.berkeley.edu
  • Received by editor(s): October 26, 1999
  • Published electronically: November 8, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 1151-1167
  • MSC (2000): Primary 35A22; Secondary 58J40, 81R30
  • DOI: https://doi.org/10.1090/S0002-9947-00-02751-3
  • MathSciNet review: 1804416