Work

Inducing Riesz Bases in $$L^2$$ via Composition Operators

Year: 2025

Type: article

Abstract: Let $$C_h$$ C h be a composition operator mapping $$L^2(\Omega _1)$$ L 2 ( Ω 1 ) into $$L^2(\Omega _2)$$ L 2 ( Ω 2 ) for some open sets $$\Omega _1, \Omega _2 \subseteq {\mathbb {R}}^n$$ Ω 1 , Ω 2 ⊆ R n . We characterize the mappings h that transform Riesz bases of $$L^2(\Omega _1)$$ L 2 ( Ω 1 ) into Riesz bases of $$L^2(\Omega _2)$$ 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.

Source: Complex Analysis and Operator Theory

DOI: 10.1007/s11785-025-01874-5

Authors: Yahya Saleh, Armin Iske

Institutions: Universität Hamburg, Deutsches Elektronen-Synchrotron DESY, Center for Free-Electron Laser Science

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Universität Hamburg