Yahya Saleh

Yahya Saleh, Armin Iske

Let $C_h$ be a composition operator mapping $L^2(Ω_1)$ into $L^2(Ω_2)$ for some open sets $Ω_1, Ω_2 \subseteq \mathbb{R}^n$. We characterize the mappings $h$ that transform Riesz bases of $L^2(Ω_1)$ into Riesz bases of $L^2(Ω_2)$. Restricting our analysis to differentiable mappings, we demonstrate that mappings $h$ that preserve Riesz bases have Jacobian determinants that are bounded away from zero and infinity. We discuss implications of these results for approximation theory, highlighting the potential of using bijective neural networks to construct Riesz bases with favorable approximation properties.