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 in | Geometric and functional analysis Vol. 32; no. 4; pp. 938 - 949 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.08.2022
Springer Nature B.V |
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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 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Kulikov, Aleksei |
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| CitedBy_id | crossref_primary_10_1103_PhysRevA_108_042410 crossref_primary_10_22331_q_2024_07_17_1414 crossref_primary_10_1090_tran_8990 crossref_primary_10_1515_ans_2022_0050 crossref_primary_10_1007_s40315_024_00566_z |
| Cites_doi | 10.1016/j.jnt.2014.11.015 10.1112/blms.12455 10.7169/facm/1680 10.1007/BF01181439 10.1007/BF01447865 10.1016/j.difgeo.2015.09.007 10.1112/blms.12183 10.4064/sm176-1-6 10.4171/ECR/18-1/18 10.1090/S0002-9904-1978-14553-4 |
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| Copyright | The Author(s) 2022 The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| References | Bondarenko, Brevig, Saksman, Seip, Zhao (CR2) 2018; 50 Hardy, Littlewood (CR5) 1927; 97 CR9 Brevig, Ortega-Cerdà, Seip, Zhao (CR3) 2018; 59 CR13 CR12 CR11 CR10 Izmestiev (CR7) 2015; 43 Schmidt (CR14) 1940; 46 Bondarenko, Heap, Seip (CR1) 2015; 150 Burbea (CR4) 1987; 31 Helson (CR6) 2006; 176 Kulikov (CR8) 2020; 53 H Helson (608_CR6) 2006; 176 608_CR11 I Izmestiev (608_CR7) 2015; 43 608_CR12 J Burbea (608_CR4) 1987; 31 608_CR13 A Bondarenko (608_CR2) 2018; 50 A Bondarenko (608_CR1) 2015; 150 A Kulikov (608_CR8) 2020; 53 608_CR9 608_CR10 OF Brevig (608_CR3) 2018; 59 E Schmidt (608_CR14) 1940; 46 GH Hardy (608_CR5) 1927; 97 |
| References_xml | – volume: 150 start-page: 191 year: 2015 end-page: 205 ident: CR1 article-title: An inequality of Hardy-Littlewood type for Dirichlet polynomials publication-title: J. Number Theory doi: 10.1016/j.jnt.2014.11.015 – volume: 53 start-page: 740 year: 2020 end-page: 746 ident: CR8 article-title: A contractive Hardy-Littlewood inequality publication-title: Bull. Lond. Math. Soc. doi: 10.1112/blms.12455 – ident: CR12 – ident: CR13 – volume: 59 start-page: 41 issue: 1 year: 2018 end-page: 56 ident: CR3 article-title: Contractive inequalities for Hardy spaces publication-title: Funct. Approx. Comment. Math. doi: 10.7169/facm/1680 – ident: CR10 – ident: CR11 – ident: CR9 – volume: 46 start-page: 204 year: 1940 end-page: 230 ident: CR14 article-title: Über die isoperimetrische Aufgabe im n-dimensionalen Raum konstanter negativer Krümmung. I. Die isoperimetrischen Ungleichungen in der hyperbolischen Ebene und fur Rotationskörper im n-dimensionalen hyperbolischen Raum publication-title: Math. Z. doi: 10.1007/BF01181439 – volume: 97 start-page: 159 issue: 1 year: 1927 end-page: 209 ident: CR5 article-title: Some new properties of Fourier constants publication-title: Math. Ann. doi: 10.1007/BF01447865 – volume: 43 start-page: 95 year: 2015 end-page: 101 ident: CR7 article-title: A simple proof of an isoperimetric inequality for Euclidean and hyperbolic cone-surfaces publication-title: Differ. Geom. Appl. doi: 10.1016/j.difgeo.2015.09.007 – volume: 31 start-page: 248 issue: 2 year: 1987 end-page: 264 ident: CR4 article-title: Sharp inequalities for holomorphic functions publication-title: Ill. J. Math. – volume: 50 start-page: 709 issue: 4 year: 2018 end-page: 724 ident: CR2 article-title: Pseudomoments of the Riemann zeta function publication-title: Bull. Lond. Math. Soc. doi: 10.1112/blms.12183 – volume: 176 start-page: 85 issue: 1 year: 2006 end-page: 92 ident: CR6 article-title: Hankel forms and sums of random variables publication-title: Studia Math. doi: 10.4064/sm176-1-6 – volume: 31 start-page: 248 issue: 2 year: 1987 ident: 608_CR4 publication-title: Ill. J. Math. – volume: 59 start-page: 41 issue: 1 year: 2018 ident: 608_CR3 publication-title: Funct. Approx. Comment. Math. doi: 10.7169/facm/1680 – volume: 46 start-page: 204 year: 1940 ident: 608_CR14 publication-title: Math. Z. doi: 10.1007/BF01181439 – volume: 43 start-page: 95 year: 2015 ident: 608_CR7 publication-title: Differ. Geom. Appl. doi: 10.1016/j.difgeo.2015.09.007 – volume: 53 start-page: 740 year: 2020 ident: 608_CR8 publication-title: Bull. Lond. Math. Soc. doi: 10.1112/blms.12455 – volume: 97 start-page: 159 issue: 1 year: 1927 ident: 608_CR5 publication-title: Math. Ann. doi: 10.1007/BF01447865 – volume: 176 start-page: 85 issue: 1 year: 2006 ident: 608_CR6 publication-title: Studia Math. doi: 10.4064/sm176-1-6 – ident: 608_CR9 doi: 10.4171/ECR/18-1/18 – volume: 50 start-page: 709 issue: 4 year: 2018 ident: 608_CR2 publication-title: Bull. Lond. Math. Soc. doi: 10.1112/blms.12183 – ident: 608_CR11 – volume: 150 start-page: 191 year: 2015 ident: 608_CR1 publication-title: J. Number Theory doi: 10.1016/j.jnt.2014.11.015 – ident: 608_CR10 – ident: 608_CR13 – ident: 608_CR12 doi: 10.1090/S0002-9904-1978-14553-4 |
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| Title | Functionals with extrema at reproducing kernels |
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