Abstract
This first chapter is devoted to the definition of Fourier-Bros-Iagolnitzer (FBI) transformation and to its application to the study of microlocal regularity of distributions. The first section studies FBI transformations with quadratic phases, as those introduced by Bros-Iagolnitzer [Br-I] and Sjöstrand [Sj]. In particular, we prove a characterization, due to P. Gérard [G], of H s microlocal regularity of distributions in terms of FBI transformations. We also give, following [H], an inversion formula due to Lebeau [L1], expressing a distribution as an integral of its FBI transform.
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© 1992 Springer-Verlag Berlin Heidelberg
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Delort, JM. (1992). Fourier-Bros-Iagolnitzer transformation and first microlocalization. In: F.B.I. Transformation. Lecture Notes in Mathematics, vol 1522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21539-5_2
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DOI: https://doi.org/10.1007/978-3-662-21539-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55764-7
Online ISBN: 978-3-662-21539-5
eBook Packages: Springer Book Archive