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, A Defant Institut für Mathematik, Carl von Ossietzky Universität , 26111 Oldenburg, Germany Search for other works by this author on: Oxford Academic D Galicer Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires and IMAS-CONICET . Ciudad Universitaria, Pabellón I (C1428EGA) C.A.B.A., Argentina Corresponding author: dgalicer@dm.uba.ar Search for other works by this author on: Oxford Academic M Mansilla Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires and IAM-CONICET . Saavedra 15 (C1083ACA) C.A.B.A., Argentina Search for other works by this author on: Oxford Academic M Mastyło Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Uniwersytetu Poznańskiego 4 , 61-614 Poznań, Poland Search for other works by this author on: Oxford Academic S Muro FCEIA, Universidad Nacional de Rosario and CIFASIS , CONICET, Ocampo & Esmeralda, S2000 Rosario, Argentina Search for other works by this author on: Oxford Academic
International Mathematics Research Notices, rnae083, https://doi.org/10.1093/imrn/rnae083
Published:
05 June 2024
Article history
Received:
23 November 2023
Revision received:
18 March 2024
Accepted:
22 March 2024
Published:
05 June 2024
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A Defant, D Galicer, M Mansilla, M Mastyło, S Muro, Asymptotic Insights for Projection, Gordon–Lewis, and Sidon Constants in Boolean Cube Function Spaces, International Mathematics Research Notices, 2024;, rnae083, https://doi.org/10.1093/imrn/rnae083
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Abstract
The main aim of this work is to study important local Banach space constants for Boolean cube function spaces. Specifically, we focus on |$\mathcal{B}_{\mathcal{S}}^{N}$|, the finite-dimensional Banach space of all real-valued functions defined on the |$N$|-dimensional Boolean cube |$\{-1, +1\}^{N}$| that have Fourier–Walsh expansions supported on a fixed family |$\mathcal{S}$| of subsets of |$\{1, \ldots , N\}$|. Our investigation centers on the projection, Sidon, and Gordon–Lewis constants of this function space. We combine tools from different areas to derive exact formulas and asymptotic estimates of these parameters for special types of families |$\mathcal{S}$| depending on the dimension |$N$| of the Boolean cube and other complexity characteristics of the support set |$\mathcal{S}$|. Using local Banach space theory, we establish the intimate relationship among these three important constants.
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