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When isf(x,y) = u(x) + v(y)?

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Abstract

LetX andY be arbitrary non-empty sets and letS a non-empty subset ofX ×Y. We give necessary and sufficient conditions onS which ensure that every real valued function onS is the sum of a function onX and a function onY.

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References

  1. Kłopotowski A, Nadkarni M G, On Transformations with simple Lebesgue spectrum,Proc. Indian Acad. Sci. (Math. Sci.) 109 (1999) 47–55

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Authors and Affiliations

  1. Department of Mathematics, University of Mumbai, 400098, Kalina, Mumbai, India

    R. C. Cowsik, A. Kłopotowski & M. G. Nadkarni

  2. Université Paris XIII, Institut Galilée, 93430, Villetaneuse cedex, France

    A. Kłopotowski

  3. Department of Mathematics, University of Mumbai, 400 098, Kalina, Mumbai, India

    M. G. Nadkarni

Authors
  1. R. C. Cowsik
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  2. A. Kłopotowski
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  3. M. G. Nadkarni
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Correspondence to R. C. Cowsik.

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Cowsik, R.C., Kłopotowski, A. & Nadkarni, M.G. When isf(x,y) = u(x) + v(y)?. Proc. Indian Acad. Sci. (Math. Sci.) 109, 57–64 (1999). https://doi.org/10.1007/BF02837767

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  • DOI: https://doi.org/10.1007/BF02837767

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