Functionals with extrema at reproducing kernels

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 Pavlović and of Brevig, Ortega-Cerdà, Seip and Zhao and the Wehrl...

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Published inGeometric and functional analysis Vol. 32; no. 4; pp. 938 - 949
Main Author Kulikov, Aleksei
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2022
Springer Nature B.V
Subjects
Analysis
Kernels
Mathematics
Mathematics and Statistics
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Summary: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 Pavlović and of Brevig, Ortega-Cerdà, Seip and Zhao and the Wehrl-type entropy conjecture for the SU (1, 1) group of Lieb and Solovej, respectively.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-022-00608-5