Functional equations for polynomials
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- by Kelly McKennon and Bruce Dearden PDF
- Proc. Amer. Math. Soc. 63 (1977), 23-28 Request permission
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
- W. H. Greub, Multilinear algebra, Die Grundlehren der mathematischen Wissenschaften, Band 136, Springer-Verlag New York, Inc., New York, 1967. MR 0224623
- William Feller, An introduction to probability theory and its applications. Vol. I, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0228020
- F. Nevanlinna and R. Nevanlinna, Absolute analysis, Die Grundlehren der mathematischen Wissenschaften, Band 102, Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by Phillip Emig. MR 0346098
Additional Information
- © Copyright 1977 American Mathematical Society
- 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