On extending C<superscript>k</superscript> functions from an open set to ℝ with applications.
In: Czechoslovak Mathematical Journal, Jg. 73 (2023-07-01), Heft 2, S. 487-498
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Zugriff:
For k ∈ ℕ ∪ {∞} and U open in ℝ, let C k (U) be the ring of real valued functions on U with the first k derivatives continuous. It is shown that for f ∈ C k (U) there is g ∈ C ∞ (ℝ) with U ⊆ coz g and h ∈ C k (ℝ) with fg∣ U = h∣ U . The function f and its k derivatives are not assumed to be bounded on U. The function g is constructed using splines based on the Mollifier function. Some consequences about the ring C k (ℝ) are deduced from this, in particular that Q cl (C k (ℝ)) = Q(C k (ℝ)). [ABSTRACT FROM AUTHOR]
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Titel: |
On extending C<superscript>k</superscript> functions from an open set to ℝ with applications.
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Autor/in / Beteiligte Person: | Burgess, Walter D. ; Raphael, Robert M. |
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Zeitschrift: | Czechoslovak Mathematical Journal, Jg. 73 (2023-07-01), Heft 2, S. 487-498 |
Veröffentlichung: | 2023 |
Medientyp: | academicJournal |
ISSN: | 0011-4642 (print) |
DOI: | 10.21136/CMJ.2023.0445-21 |
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