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Hankel transforms and weak dispersion

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2019-20 MATRIX Annals

Part of the book series: MATRIX Book Series ((MXBS,volume 4))

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Abstract

This survey is concerned with a general strategy, based on Hankel transforms and special functions decompositions, to prove weak dispersive estimates for a class of PDE's. Inspired by [2], we show how to adapt the method to some scaling critical dispersive models, as the Dirac-Coulomb equation and the fractional Schr¨odinger and Dirac equation in Aharonov-Bohm field.

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Acknowledgements

The authors are grateful to Kenji Nakanishi for providing several useful comments and suggestions. The first author is partially supported by the University of Padova STARS project “Linear and Nonlinear Problems for the Dirac Equation” (LANPDE).

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitä degli studi di Padova, Via Trieste, 63, 35131, Padova PD,, Italy

    Federico Cacciafesta

  2. Universidad del País Vasco - Euskal Herriko Unibertsitatea & Ikerbasque,, Bilbao, Spain

    Luca Fanelli

Authors
  1. Federico Cacciafesta
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  2. Luca Fanelli
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Corresponding author

Correspondence to Federico Cacciafesta .

Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, University of Melbourne, Parkville, VIC, Australia

    Jan de Gier

  2. Department of Mathematics and Statistics, The University of Western Australia, Melbourne, Australia

    Cheryl E. Praeger

  3. Department of Mathematics, University of California Los Angeles, Los Angeles, CA, USA

    Terence Tao

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Cacciafesta, F., Fanelli, L. (2021). Hankel transforms and weak dispersion. In: de Gier, J., Praeger, C.E., Tao, T. (eds) 2019-20 MATRIX Annals. MATRIX Book Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-62497-2_62

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