Lichawski-Matkowski-Miś theorem on locally defined operators for functions of several variables

Authors

  • Małgorzata Wróbel Institute of Mathematics and Informatics, Jan Długosz University, Armii Krajowej 13/15, 42-218 Częstochowa, Poland

Abstract

Let D be a regular closed set in the open subspace G ⊂ ℝⁿ and Cᵐ(D) be the space of functions f|D such that f ∈ Cᵐ(G). The representation formulas for locally defined operators mapping Cᵐ(D) into C⁰(D) and into C¹(D) are given.

References

K. Lichawski, J. Matkowski, J. Miś, Locally defined operators in the space of differentiable functions, Bull. Polish Acad. Sci. Math. 37 (1989), no. 1-6, 315-325.
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H. Whitney, Analytic extensions of differentiable functions defined in closed sets, Trans. Amer. Math. Soc. 36 (1934), no. 1, 63-89.
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M. Wróbel, Some consequences of locally defined operators, in: Proceedings of the XIIth Czech–Polish–Slovak Mathematical School, Faculty of Education of University J.E. Purkyně in Ústi nad Labem, 2005, 82-86.
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Published

2008-11-08

How to Cite

Wróbel, M. (2008). Lichawski-Matkowski-Miś theorem on locally defined operators for functions of several variables. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 7, 15–22. Retrieved from https://studmath.uken.krakow.pl/article/view/13265

Issue

Vol. 7 (2008): Annales Academiae Paedagogicae Cracoviensis Studia Mathematica

Section

Published