Interpolation and extrapolation of smooth functions by linear operators

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Whitney’s extension problem for $C^m$ (2006, background): “thanks to Brudnyi and Shvartsman [3,...,7 and 14,15,16], and my own papers [ 8 ,9,11].”
A sharp form of Whitney's extension theorem (2005, background): “A forthcoming paper [ 7 ] will settle some of the issues raised by Brudnyi and Shvartsman, to whom I am grateful for bringing these matters to my attention.”
Testing the Manifold Hypothesis (2013, methodology): “By Theorem 1 of [23] we know the following.”