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arXiv · 2203.12349

Functionals with extrema at reproducing kernels

Aleksei Kulikov
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Abstract

We show that certain monotone functionals on the Hardy spaces and convex functionals on the Bergman spaces are maximized at the normalized reproducing kernels among the functions of norm $1$, thus proving the contractivity conjecture of Pavlovi\'c and of Brevig, Ortega-Cerd\`a, Seip and Zhao and the Wehrl-type entropy conjecture for the $SU(1,1)$ group of Lieb and Solovej, respectively.

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Aleksei Kulikov. 2022-03-23. Functionals with extrema at reproducing kernels. https://arxiv.org/abs/2203.12349

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