Banach-Lamperti for Kurzweil-Henstock
Thierry De Pauw
TL;DR
This paper characterizes the isometric isomorphisms of Kurzweil-Henstock integrable functions as transformations that are bi-absolutely continuous, providing a structural understanding of these function spaces.
Contribution
It establishes a Banach-Lamperti type theorem for Kurzweil-Henstock integrable functions, identifying their isometric isomorphisms with specific variable changes.
Findings
Isometric isomorphisms correspond to bi-absolutely-continuous changes of variable.
Provides a Banach-Lamperti theorem for Kurzweil-Henstock integrable functions.
Enhances understanding of the structure of Kurzweil-Henstock function spaces.
Abstract
We identify isometric isomorphisms of the space of Kurzweil-Henstock integrable functions as bi-absolutely-continuous changes of variable.
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Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Nonlinear Differential Equations Analysis