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

• Autorzy: Wróbel Małgorzata

Identyfikatory

DOI

10.17512/jamcm.2022.2.09

• Języki publikacji: EN

Abstrakty

EN

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 × R^N → R.

Słowa kluczowe

EN

locally defined operators; function of the class C∞ in the Whitney sense; m-times Whitney continuously differentiable function

PL

operator zdefiniowany lokalnie

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 2
• Strony: 103--110
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Wróbel Małgorzata

• Department of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

• [1] Wróbel, M., (2013). Locally defined operators in the space of functions of bounded phi-variation. Real Anal. Exch., 38(1), 79-94.
• [2] Wróbel, M. (2012). Uniformly bounded Nemytskij operators between the Banach spaces of functions of bounded n-th variation. J. Math. Anal. Appl.., 391, 451-456.
• [3] Lichawski, K., Matkowski, J., & Mi ́s, J. (1989). Locally defined operators in the space of differentiable functions. Bull. Polish Acad. Sci. Math., 37, 315-325.
• [4] Matkowski, J., & Wr ́obel, M. (2008). Locally defined operators in the space of Whitney differentiable functions. Nonlinear Anal. TMA, 68(10), 2873-3232.
• [5] Brunner, H. (2017). Volterra Integral Equations. Cambridge University Press.
• [6] Regan, D., & Meehan, M. (1998). Existence Theory for Nonlinear Integral and Integrodifferential Equations. Dordrecht: Kluwer Academic.
• [7] Khan, K.A. (2019). Whitney differentiability of optimal-value functions for bound-constrained convex programming problems. Optimization, 68(2-3), 691-711.
• [8] Whitney, W. (1934). Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc., 36, 63-89.
• [9] Malgrange, B. (1966). Ideals of Differentiable Functions. Oxford University Press.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).