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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Functional equations for polynomials


Authors: Kelly McKennon and Bruce Dearden
Journal: Proc. Amer. Math. Soc. 63 (1977), 23-28
MSC: Primary 15A69
DOI: https://doi.org/10.1090/S0002-9939-1977-0437566-9
MathSciNet review: 0437566
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Abstract: The set of all continuous symmetric multilinear forms of degree m on a real topological vector space V are shown to be in one-to-one correspondence with the family of continuous scalar-valued functions on V satisfying a certain functional equation. If V is n-dimensional, these functions are precisely those which can be represented by m-homogeneous polynomials of degree n (with respect to some basis of V).

The connection between this family of generalized polynomials and the mth derivatives of a scalar-valued function is discussed.


References [Enhancements On Off] (What's this?)

  • [1] W. H. Greub, Multilinear algebra, Die Grundlehren der Mathematischen Wissenschaften, Band 136, Springer-Verlag New York, Inc., New York, 1967. MR 0224623
  • [2] William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
  • [3] F. Nevanlinna and R. Nevanlinna, Absolute analysis, Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by Phillip Emig; Die Grundlehren der mathematischen Wissenschaften, Band 102. MR 0346098

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DOI: https://doi.org/10.1090/S0002-9939-1977-0437566-9
Article copyright: © Copyright 1977 American Mathematical Society