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A general approximation theorem of Whitney type.

Michael Langenbruch (2003)


We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions...

A limit involving functions in W 0 1 , p ( Ω )

Biagio Ricceri (1999)

Colloquium Mathematicae

We point out the following fact: if Ω ⊂ n is a bounded open set, δ>0, and p>1, then l i m 0 + i n f V Ω | ( x ) | p d x = , where V = W 0 1 , p ( Ω ) : m e a s ( x Ω : | ( x ) | > δ ) > .

A Paley-Wiener type theorem for generalized non-quasianalytic classes

Jordi Juan-Huguet (2012)

Studia Mathematica

Let P be a hypoelliptic polynomial. We consider classes of ultradifferentiable functions with respect to the iterates of the partial differential operator P(D) and prove that such classes satisfy a Paley-Wiener type theorem. These classes and the corresponding test spaces are nuclear.

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