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SUMMARY:Ivan S. Trapasso (Università di Genova)
DTSTART:20210421T160000Z
DTEND:20210421T170000Z
DTSTAMP:20260423T052805Z
UID:HAeS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HAeS/15/">Di
 spersion\, spreading and sparsity of Gabor wave packets</a>\nby Ivan S. Tr
 apasso (Università di Genova) as part of Harmonic analysis e-seminars\n\n
 \nAbstract\nSparsity properties for phase-space representations of several
  types of operators (including pseudodifferential\, metaplectic and Fourie
 r integral operators) have been extensively studied in recent articles\, w
 ith applications to the analysis of dispersive evolution equation. It has 
 been proved that such operators are approximately diagonalized by Gabor wa
 ve packets - equivalently\, the corresponding phase-space representations 
 (Gabor matrix/kernel) can be thought of as sparse infinite-dimensional mat
 rices. While wave packets are expected to undergo some spreading and dispe
 rsion phenomena\, there is no record of these issues in the aforementioned
  estimates. We recently proved refined estimates for the Gabor matrix of m
 etaplectic operators\, also of generalized type\, where sparsity\, spreadi
 ng and dispersive properties are all simultaneously noticeable. We also pr
 ovide applications to the propagation of singularities for the Schr\\"odin
 ger equation\; in this connection\, our results can be regarded as a micro
 local refinement of known estimates. The talk is based on joint work with 
 Elena Cordero and Fabio Nicola.\n
LOCATION:https://researchseminars.org/talk/HAeS/15/
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