A divided-difference characterization of polynomials over a general field
(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) It is proved that, for an arbitrary field K not of characteristic 2 and arbitrary ..., if functions f : K[arrow right]K and h : K[arrow right]K satisfy f [x^sub 1^, . . . , x^sub n^] = h (x^sub 1^ + . . . + x^sub n^) wheneve...
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| Veröffentlicht in: | Aequationes mathematicae 1998-02, Vol.55 (1), p.73-78 |
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| container_title | Aequationes mathematicae |
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| creator | Davies, R. O. Rousseau, G. |
| description | (ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image) It is proved that, for an arbitrary field K not of characteristic 2 and arbitrary ..., if functions f : K[arrow right]K and h : K[arrow right]K satisfy f [x^sub 1^, . . . , x^sub n^] = h (x^sub 1^ + . . . + x^sub n^) whenever x^sub 1^, . . . , x^sub n^ are distinct elements of K, then f is equal to a polynomial of degree at most n over K. (Here f [x^sub 1^, . . . , x^sub n^] denotes the divided difference of f at the distinct points x^sub 1^, . . . , x^sub n^.) The case of a field of characteristic 2 is also considered. [PUBLICATION ABSTRACT] |
| doi_str_mv | 10.1007/PL00000046 |
| format | Article |
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| title | A divided-difference characterization of polynomials over a general field |
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