Monatshefte für Mathematik

, Volume 175, Issue 4, pp 639–643 | Cite as

On Fréchet’s functional equation

  • László SzékelyhidiEmail author


Fréchet’s functional equation \(\Delta _{y_1,y_2,\dots ,y_{n+1}}f=0\) plays a key role in the theory of polynomial functions. A basic theorem of Djokovič shows that under general conditions the functional equation \(\Delta _y^{n+1}f=0\) is equivalent to Fréchet’s equation. Here we give a short alternative proof for this result using spectral synthesis.


Fréchet’s functional equation Spectral synthesis 

Mathematics Subject Classification (2000)

39A70 39A99 


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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary
  2. 2.Department of MathematicsUniversity of BotswanaGaboroneBotswana

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