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X-ORIGINAL-URL:https://cmc.deusto.eus/
X-WR-CALNAME:cmc.deusto.eus
X-WR-CALDESC:DeustoCCM - Chair of Computational Mathematics at University of Deusto
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CLASS:PUBLIC
UID:MEC-a90f92d5609224ee7112c1f5d99f7e5f@cmc.deusto.eus
DTSTART:20211209T100000Z
DTEND:20211209T103000Z
DTSTAMP:20211207T122500Z
CREATED:20211207
LAST-MODIFIED:20220117
PRIORITY:5
TRANSP:OPAQUE
SUMMARY:Fourier multipliers, Hausdorff measure and classification with scattering transform
DESCRIPTION:Next Thursday December 9, Javier Minguillón Sánchez, ERC-DyCon Internship student at UAM will talk on “Fourier multipliers, Hausdorff measure and classification with scattering transform” as part of our DeustoCCM’s seminars.\nWHEN?\nThursday December 9, 2021 at 11:00H\nAbstract. We begin by defining what a Fourier multiplier operator is and state some important properties. After that we give several examples of operators, out of which the most relevant are the disk multiplier and the spherical multiplier.\nThen we proceed to discuss the boundedness of the disk operator and the spherical maximal operator. The first one is related to a counterexample due to Fefferman. For the second one, we use a result of Rubio de Francia.\nWe move on to define the Hausdorff measure and Hausdorff dimension on  \mathbb{R}^d. We state several results:\nFrostman’s Lemma, one result about constructing sets of arbitrary dimension, and another one about the projection of Borel sets onto lines.\nAfter that we talk a bit about funcional data statistics and discuss in detail the Principal Components Analysis method. We give its theoretical basis (Karhunen-Loève’s Theorem).\nAs a closure, we define the scattering transform of a function with domain in \mathbb {R}^2 . We explain how to classify images with the above and the help of principal components analysis.\nthe help of principal components analysis.\n
URL:https://cmc.deusto.eus/events-calendar/fourier-multipliers-hausdorff-measure-and-classification-with-scattering-transform/
ORGANIZER;CN=DeustoCCM - Chair of Computational Mathematics:MAILTO:
CATEGORIES:Events Calendar,Events Calendar Past
ATTACH;FMTTYPE=image/png:https://cmc.deusto.eus/wp-content/uploads/2021/12/DeustoCCMseminar-jMinguillon-09dic2021.png
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