Functional equations for polynomials
Kelly McKennon and Bruce Dearden
Proc. Amer. Math. Soc. 63 (1977), 23-28
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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.
H. Greub, Multilinear algebra, Die Grundlehren der
Mathematischen Wissenschaften, Band 136, Springer-Verlag New York, Inc.,
New York, 1967. MR 0224623
Feller, An introduction to probability theory and its applications.
Vol. I, Third edition, John Wiley & Sons, Inc., New
York-London-Sydney, 1968. MR 0228020
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
- W. H. Greub, Multilinear algebra, Springer-Verlag, Berlin and New York, 1967. MR 37 #222. MR 0224623 (37:222)
- 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)
- 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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