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Friday, April 19, 2019
5:00 PM - 5:50 PM

Caltech/UCLA Joint Analysis Seminar

Weissler's conjecture on the Boolean cube
Paata Ivanisvili, Department of Mathematics, UC Irvine,
UCLA MS 6627

The necessary and sufficient conditions will be obtained on L p Lp L^p to L q Lq L^q boundedness of the Hermite semigroup e zΔ ezΔ e^{z\Delta} on the boolean cube of an arbitrary dimension equipped with uniform counting measure, where z z z is a complex number and 1≤pq 1≤p≤q 1\leq p \leq q . This solves an old open problem in complex hypercontractivity theory on the Hamming. Certain cases of the triples (p,q,z) (p,q,z) (p,q,z) were characterized by Bonami (1970); Beckner (1975); and Weissler (1979). Several applications will be presented. Work in progress with Fedja Nazarov.

For more information, please contact Math Dept. by phone at 626-395-4335 or by email at mathinfo@caltech.edu.