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Ramesh Manna

Wednesday, September 16, 2020 - 15:30 to 16:30
SMS Conference Room (via GoogleMeet)
Ramesh Manna
Indian Institute of Science
Fourier integral operator, unique continuation property (UCP) and momentum ray transforms

In this talk, we prove the local smoothing estimate for Fourier integral operators with phase function $h(x, t, \xi)= x . \xi + t|\xi|$, and amplitude function $a(x,t, \xi)$ belongs to $S^m$, the symbol class of order m less or equal to 0. Such Fourier integral operators arise in wave equation and also in the study of spherical maximal operators. We give an overview of the regularity results which have been proven to date. We use harmonic analysis of Hermite functions in the study of Fourier integral operators.
Then, we discuss the unique continuation property(UCP) for Baouendi Grushin operators and the heat equation. Finally, we briefly discuss momentum ray transforms that are Fourier integral operators in the context of inverse problems in integral geometry.

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