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We characterize the validity of the Whitney extension theorem in the ultradifferentiable Roumieu setting with controlled loss of regularity. Specifically, we show that in the main Theorem 1.3 of [15] condition (1.3) can be dropped. Moreover, we clarify some questions that remained open in [15].
In this memoir, we develop a general framework which allows for a simultaneous study of labeled and unlabeled near alignment data problems in $mathbb R^D$ and the Whitney near isometry extension problem for discrete and non-discrete subsets of $mathb
Let $ f $ be a real-valued function on a compact subset in $ mathbb{R}^n $. We show how to decide if $ f $ extends to a nonnegative and $ C^1 $ function on $ mathbb{R}^n $. There has been no known result for nonnegative $ C^m $ extension from a gener
A classical theorem of Kuratowski says that every Baire one function on a G_delta subspace of a Polish (= separable completely metrizable) space X can be extended to a Baire one function on X. Kechris and Louveau introduced a finer gradation of Baire
We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we
We prove an analogue of Chernoffs theorem for the Laplacian $ Delta_{mathbb{H}} $ on the Heisenberg group $ mathbb{H}^n.$ As an application, we prove Ingham type theorems for the group Fourier transform on $ mathbb{H}^n $ and also for the spectral projections associated to the sublaplacian.