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DTSTART:20200308T060000
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DTSTART;TZID=America/Halifax:20201030T160000
DTEND;TZID=America/Halifax:20201030T170000
DTSTAMP:20260609T083529
CREATED:20200904T115630Z
LAST-MODIFIED:20201116T135614Z
UID:5468-1604073600-1604077200@aarms.math.ca
SUMMARY:Dalhousie-AARMS AAMP Seminar: Jean-Pierre Garbardo (McMaster University)
DESCRIPTION:Title: Factorization of positive definite functions through convolution and the Turàn problem\n Abstract: If  is a finite abelian group\, we call a subset  symmetric if  and  whenever . We also let . We consider the problem of expressing an arbitrary positive definite function  on  as the convolution product of two positive definite functions\, one supported on  and the other one supported on . We show that\, in the particular case where  is the constant function \, this problem is related to the Tur\’an problem for positive definite functions. In the particular case of a finite abelian group\, this last problem asks the following question. Given a symmetric set \, find the maximum value of the sum  if  and  is a positive definite function on  supported on . We introduce the notion of  {\it dual Tur\’an problem for }\, which is essentially the Tur\’an problem for the set \, and show how the Tur\’an problem for  and its dual are related\, and how the factorization mentioned above plays a role is solving both those problems. We will then give an overview of how these results can be extended to other abelian groups such as . \nThe Dalhousie-AARMS Analysis-Applied Math-Physics Seminar takes place on Fridays from 4 – 5 pm Atlantic Time over Zoom.  If you would like to attend\, please email the organizers for connection details.
URL:https://aarms.math.ca/event/dalhousie-aarms-aamp-seminar-2020-10-16-2-2/
LOCATION:Zoom seminar
CATEGORIES:AAMP Seminar
ORGANIZER;CN="Suresh%20Eswarathasan":MAILTO:sr766936@dal.ca
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