Asymptotic insights for projection, Gordon-Lewis and Sidon constants in Boolean cube function spaces
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911885248430080 |
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| author | Defant, Andreas Galicer, Daniel Mansilla, Martín Mastyło, Mieczysław Muro, Santiago |
| author_facet | Defant, Andreas Galicer, Daniel Mansilla, Martín Mastyło, Mieczysław Muro, Santiago |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_00233 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic insights for projection, Gordon-Lewis and Sidon constants in Boolean cube function spaces Defant, Andreas Galicer, Daniel Mansilla, Martín Mastyło, Mieczysław Muro, Santiago Functional Analysis Metric Geometry Primary: 06E30, 46B06, 46B07. Secondary: 42A16, 43A75 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. |
| title | Asymptotic insights for projection, Gordon-Lewis and Sidon constants in Boolean cube function spaces |
| topic | Functional Analysis Metric Geometry Primary: 06E30, 46B06, 46B07. Secondary: 42A16, 43A75 |
| url | https://arxiv.org/abs/2302.00233 |