Some Oscillatory Operators and Multipliers in Harmonic Analysis and discrete Painlevé equations-China University of Mining & Technology-Beijing-China University of Mining & Technology-Beijing

Some Oscillatory Operators and Multipliers in Harmonic Analysis and discrete Painlevé equations

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speaker: Dashan Fan, University of Wisconsin-Milwaukee, Professor

time: 2024.5.28，2:00PM

place: Tencent Meeting: 283-435-710

Abstract:

Bochner-Riesz means, Stein's spherical maximal operator, Schrödinger operator, wave operator, the solution of the Klein-Gordon equation, the solution of damped wave equation, etc. are among some most important operators in harmonic analysis. All these operators are related to the strongly singular integral and some oscillating integrals, and they are also closely related to the 4 great conjectures in Harmonic Analysis. In the talk, we briefly introduce the origins and backgrounds of these operators and describe the intrinsic connections of these operators. We also address an unsolved problem of Stein's spherical maximal operator that is related to Sogge's local smoothing conjecture.

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