Inducing Riesz and orthonormal bases in L2 via composition operators
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Abstract (arXiv)
Let Ch be a composition operator mapping L2(Omega1) into L2(Omega2) for some open sets Omega1, Omega2 subseteq ℝn. We characterize the mappings h that transform Riesz bases of L2(Omega1) into Riesz bases of L2(Omega2). 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.
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References · 5
- 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
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- 2019Inferring the quantum density matrix with machine learningcited by 8
- 2023Computing excited states of molecules using normalizing flowscited by 4
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