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Fourth Prairie Analysis
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Bus Transportation in Lawrence
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Talks and AbstractsStephen WaingerSome discrete problems in Harmonic AnalysisWe will discuss certain problems of harmonic analysis that employ methods of analytic number theory. These problems concern l^p estimates for operators defined on functions on Z^d-points in R^d with integer coordinates or discrete subgroups of homogeneous groups. This subject was originated simultaneously by Arkhipov and Oskolkov and Bourgain. We will briefly discuss their work, and we will mention some recent joint results with Ionescu, Magyar and Stein. Extended Abstract (pdf file)
Loukas GrafakosRecent results on maximal multipliersA bounded function on a euclidean space is called a Hormander multiplier if it is differentiable up to a certain order and its mth derivative times the mth power of its argument is bounded for all m up to its order of differentiability. A question addressed is whether the supremum of the family of linear multiplier operators obtained from the dilation of a single Hormander multiplier is L^p bounded. Analogous questions are studied for families of linear operators with Hormander multipliers that satisfy the definition uniformly. This is joint work with Michael Christ, Petr Honzik, and Andreas Seeger.
Akos MagyarSome Ramsey type results on lattice pointsA result of Katznelson and Weiss says that all large positive numbers occur as distances between points of measurable subset of R^n of positive density. We prove a discrete analogue; if subset of Z^n of positive density $\epsilon$ is given, then the squares of distances between its points contain all large multiples of a natural number which depends only on $\epsilon$. If time permits we show that such a set contain infinitely many copies of any given k- simplex of lattice points, up to dilations and rotations, if the dimension n is large enough w.r.t. k.
Organizers:Estela A. Gavosto, KUMarianne Korten, KSU Charles Moore, KSU Rodolfo H. Torres, KU |
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