Schauder and Riesz Bases for Higher-Dimensional Lebesgue Spaces Inspired by ReLU Neural Networks 7R33E8515R

URI	`m2://res/7R33E8515R`
Kind	preprint
Creators	Julian Billner, Cornelia Schneider
Date	2026-10-09
MSC	46-XX, 30-XX, 32-XX, 11-XX
Subjects	arxiv math.FA, arxiv math.CV, arxiv math.NT
Scope	in

Expressions

e1: version, preprint

Language	en
Date	2026-10-09
Ids	arXiv 2610.14266

Items in this resource

The mentions of the inventory that name this resource. Each name links to the card of its inventory row.

Item	Kind	Where	Source
\textbf{The operators $R$ and $T_\tau^R$	definition	definition 2.21	arxiv
\textbf{Sum and scale operators $T_\tau$	statement	theorem 2.4	arxiv
\textbf{A Wiener-type basis criterion	statement	corollary 2.11	arxiv
Main result, informal version	statement	theorem 1.3	arxiv
\textbf{Surjectivity of $T_\tau$	statement	lemma 2.14	arxiv
3074N7T5E0	example	example 2.24	arxiv
\textbf{The main bases	statement	lemma 2.8	arxiv
\textbf{Solutions of} $kJ=N$	statement	lemma 2.1	arxiv
\textbf{Schauder and Riesz basis	definition	definition 1.1	arxiv
\textbf{Algebraic structure of $\{T_\tau:\tau \in \ell_1\}$	statement	theorem 2.5	arxiv
\textbf{Properties of the $d$-Dirichlet convolution	statement	lemma 2.3	arxiv
\textbf{Basis properties of $\mathcal R_d$	statement	theorem 3.5	arxiv
CHWDFCNMTK	statement	lemma 2.18	arxiv
\textbf{Spectra of the truncated Gram matrices	statement	theorem 3.4	arxiv
Algebraic behaviour of $T_\tau+T_\lambda^R$	statement	lemma 2.23	arxiv
\textbf{Invertibility of }$T_\tau$	statement	theorem 2.6	arxiv
\textbf{Similarity of sub-matrices	statement	lemma 3.3	arxiv
\textbf{The sequence spaces} $\hat\ell_d$	statement	proposition 2.17	arxiv
\textbf{Coefficients	statement	proposition 2.13	arxiv
\textbf{Scalar products of $\mathcal C_\alpha, \mathcal S_\alpha$	statement	theorem 3.2	arxiv
\textbf{The Hilbert case	statement	lemma 2.15	arxiv
$d$\textbf{-Dirichlet convolution	definition	definition 2.2	arxiv
Basis criteria	statement	theorem 2.10	arxiv
\textbf{Mixed system operator	statement	lemma 2.22	arxiv
\textbf{Mixed systems	statement	theorem 2.20	arxiv
\textbf{Double Argument Theorem for $\mathcal C$	statement	lemma 3.1	arxiv
VD16FKK1EZ	statement	theorem	arxiv
\textbf{Properties of $\mathcal Z^\tau$	statement	lemma 2.9	arxiv
\textbf{$\mathcal C, \mathcal S$	definition	definition 1.2	arxiv

Catalogue records

arxiv: 2610.14266 (work)
arxiv_text: 2610.14266 (work)