Whitney extensions on symmetric spaces
Birgit Speh, Peter Vang Uttenthal

TL;DR
This paper extends Whitney's classical function extension problem to symmetric spaces using harmonic analysis and representation theory, broadening the scope of Whitney extension theorems beyond Euclidean spaces.
Contribution
It establishes Whitney type extension theorems for functions on homogeneous spaces, utilizing harmonic analysis and representation theory of reductive groups.
Findings
Proves Whitney extension theorems on certain symmetric spaces.
Employs harmonic analysis and representation theory techniques.
Extends classical Euclidean results to non-Euclidean homogeneous spaces.
Abstract
In 1934, H. Whitney introduced the problem of extending a function on a set of points in to an analytic function on the ambient space. In this article we prove Whitney type extension theorems for data on some homogeneous spaces. We use harmonic analysis on the homogeneous spaces and representation theory of compact as well as noncompact reductive groups.
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Taxonomy
TopicsAdvanced Banach Space Theory · Fixed Point Theorems Analysis · Advanced Differential Geometry Research
MethodsSparse Evolutionary Training
