2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68761Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times differentiable so is the extension (likewise for analyticity and the class k+alpha).12 pagesFunctional AnalysisRepresentation Theory15A18; 15A42; 47A55text