Extremal Problems in Harmonic Analysis, Convexity, and Bellman Functions

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combinatorics functional analysis general mathematics optimization and control


Audience: Researchers in the topic
Conference dates: 28-Nov-2022 to 02-Dec-2022
Curator: Shadira Presbot*
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Extremal problems in harmonic analysis recently acquired prominence in questions ranging from optimizers in Fourier restriction results to sharp geometric inequalities to sharp estimates of various singular operators of Calderón–Zygmund type. Sharp inequalities and their stability versions reveal new connections between harmonic analysis, geometric measure theory, additive combinatorics, and stochastic optimal control. There are many examples of sharp estimates by stochastic control approach and the use of special types of convexity and Monge–Ampére equation. There are interesting examples of using the computational tools in proving sharp geometric inequalities for martingales and on Hamming cube and for Fourier restriction inequalities.

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