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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
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, Springer-Verlag, Berlin and New York, 1967. MR 37 #222. MR 0224623 (37:222)
  • [2] W. Feller, An introduction to probability theory and its applications, Vol. I, 3rd ed., Wiley, New York, London, and Sydney, 1968. MR 37 #3604. MR 0228020 (37:3604)
  • [3] F. Nevanlinna and R. Nevanlinna, Absolute analysis, Springer-Verlag, Berlin and New York, 1973. MR 49 #10824. MR 0346098 (49:10824)

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Article copyright: © Copyright 1977 American Mathematical Society

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