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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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


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:
  • Maciej Zworski
  • Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
  • MR Author ID: 227055
  • Email:
  • 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:
  • MathSciNet review: 1804416