Real analytic approximations which almost preserve Lipschitz constants of functions defined on the Hilbert space

2010/12/20 by Daniel Azagra, Azagra, D., R. Fry +3
Computer Science · Mathematics · #46B20 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1012.4339

openalex publication_date 2010/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a separable real Hilbert space. We show that for every Lipschitz function f:X→ℝ, and for every ε>0, there exists a Lipschitz, real analytic function g:X→ℝ such that |f(x)-g(x)|≤ ε and \textrmLip(g)≤ \textrmLip(f)+ε.

Related

• Real analytic approximation of Lipschitz functions on Hilbert space and other Banach spaces
• Approximation by Lipschitz, analytic maps on certain Banach spaces
• Approximation of functions and their derivatives by analytic maps on certain Banach spaces
• Approximation by Lipschitz functions
• The approximation property for spaces of Lipschitz functions