I am interested in finding the functions $f:\mathbb{R}^n \to \mathbb{R}^n$ for which $f \circ U = U \circ f$ for all orthogonal transformations $U:\mathbb{R}^n \to \mathbb{R}^n$. Note that $f$ need not be linear. Any ideas on the conditions on $f$ ?
2026-02-22 19:50:23.1771789823
Functions on $\mathbb{R}^n$ commuting with orthogonal transformations
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