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Proceedings of the American Mathematical Society
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0437566-9
PII: S 0002-9939(1977)0437566-9
Article copyright: © Copyright 1977 American Mathematical Society