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The FBI transform on compact ${\mathcal{C}^\infty}$ manifolds


Authors: Jared Wunsch and Maciej Zworski
Journal: Trans. Amer. Math. Soc. 353 (2001), 1151-1167
MSC (2000): Primary 35A22; Secondary 58J40, 81R30
Published electronically: November 8, 2000
MathSciNet review: 1804416
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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 ``scattering calculus'' 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
Email: zworski@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02751-3
Keywords: FBI transform, Fourier-Bros-Iagolnitzer transformation, wave-packet
Received by editor(s): October 26, 1999
Published electronically: November 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society