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Locally defined operators acting C∞ (A) into C0 (A)

Wróbel Małgorzata

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 2

103--110

We investigate the locally defined operators, sometimes called operators with memory, that map the space C∞ (A) of continuously differentiable functions in the sense of Whitney defined on a compact subset A ⊂ Rn into the space of continuous functions defined on the same set A. Using the Whitney Extension Theorem, we give a representation formula for such operators stating that every local operator K : C∞ (A) → C0 (A) is a generalized Nemytskii operator generated by some function h : A × RN → R.