On a characterization of polynomials by divided differences |
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Authors: | Jens Schwaiger |
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Institution: | (1) Institut für Mathematik, Karl-Franzens-Universität, A-8010 Graz, Austria |
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Abstract: | Summary We consider the functional equationfx
1,x
2, , x
n
] =h(x
1 + +x
n
) (x
1, ,x
n
K, x
j
x
k
forj k), (D) wherefx
1,x
2, ,x
n
] denotes the (n – 1)-st divided difference off and prove
Theorem. Let n be an integer, n 2, let K be a field, char(K) 2, with # K 8(n – 2) + 2. Let, furthermore, f, h: K K be functions. Then we have that f, h fulfil (D) if, and only if, there are constants aj K, 0 j n (a := an, b := an – 1) such thatf = ax
n
+bx
n – 1 + +a
0
and h = ax + b. |
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Keywords: | 39B52 |
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