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Representation theorem for locally defined operators in the space of Whitney differentiable functions

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Abstract

Under the assumption that \({A\subset\mathbb{R}^{n}}\) is perfect, a representation theorem for locally defined operators mapping the space C m(A) of Whitney differentiable functions into C 1(A) is given and an open problem is presented.

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Authors and Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Podgórna 50, 65246, Zielona Góra, Poland

    Janusz Matkowski

  2. Institute of Mathematics, Silesian University, Bankowa 14, 40007, Katowice, Poland

    Janusz Matkowski

  3. Institute of Mathematics and Informatics, Jan Długosz University, Armii Krajowej 13/15, 42200, Częstochowa, Poland

    Małgorzata Wróbel

Authors
  1. Janusz Matkowski
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  2. Małgorzata Wróbel
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Correspondence to Janusz Matkowski.

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Matkowski, J., Wróbel, M. Representation theorem for locally defined operators in the space of Whitney differentiable functions. manuscripta math. 129, 437–448 (2009). https://doi.org/10.1007/s00229-009-0283-2

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  • DOI: https://doi.org/10.1007/s00229-009-0283-2

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