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A Sharpened Inequality for Twisted Convolution

PDE and Applied Math Seminar

Speaker: Kevin O'Neill, UC Berkeley
Related Webpage: https://math.berkeley.edu/~oneill/index.html
Location: 2112 MSB
Start time: Fri, Jan 25 2019, 4:10PM

In the 1970's, Beckner and Brascamp-Lieb determined the optimal constant for Young's convolution inequality and showed that equality in the sharp version is attained if and only if the given functions are compatible tuples of Gaussians. Recent work by Christ establishes a quantitative stability theorem for Young's inequality, also known as a sharpened inequality. In this talk, we prove a sharpened inequality for the related trilinear form for twisted convolution, an operation related to convolution on the Heisenberg group. While no maximizers exist for twisted convolution (Beckner and Klein-Russo), we derive such an inequality by varying the oscillatory factor and expanding about the case with zero oscillation. This work quantifies a stability result previously proven by Christ.