English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the projection constant$\boldsymbol{\lambda}\big(\mathcal{B}_{\mathcal{S}}^N\big)$ of thefinite-dimensional Banach space $\mathcal{B}_{\mathcal{S}}^N$ of allreal-valued functions defined on the $N$-dimensional Boolean cube $\{-1,+1\}^N$ that have Fourier-Walsh expansions supported on a~family $\mathcal{S}$of subsets of $\{1, \ldots, N\}$. We combine ideas and tools from Fourieranalysis, combinatorics, probability, and number theory to derive exactformulas and asymptotic estimates of$\boldsymbol{\lambda}\big(\mathcal{B}_{\mathcal{S}}^N\big)$ for special typesof families $\mathcal{S}$ depending on the dimension $N$ of the Boolean cubeand other complexity parameters of $\mathcal{S}$. One of the main resultsstates that if $\mathcal{S}= \{S:\, \text{card}(S) = d\}$ or $\mathcal{S}= \{S:\, \text{card}(S) \leq d\}$, then $N^{-d/2}\boldsymbol{\lambda}\big(\mathcal{B}_{\mathcal{S}}^N\big) \to \frac{1}{2\pi}\int_{\mathbb{R}} |P_d(t)| \exp(-t^2/2)\,d\!t$ as $N\to \infty$, where $P_d$ isa concrete real polynomial of one variable. Using local Banach space theory, weshow that the Sidon, Gordon-Lewis and the projection constants of each Banachspace $\mathcal{B}_{\mathcal{ S}}^N$ are closely related.

Asymptotic estimates of projection and Sidon constants for spaces of functions on the Boolean cube