Waring's Theorem (Analysis)
The Waring set is a mathematical theorem from the mathematical sub-area of the analysis corresponding to the mathematician Edward Waring is allocated. The sentence is closely related to the sentence of Rolle .
Formulation of the sentence
The sentence can be stated as follows:
- Let a real polynomial function and three real numbers be given .
-
The following should apply:
- (I) .
- (II) and are zeros of .
- (III) There is no zero of in the open interval .
- (IV) is the associated polynomial function with .
- Then:
literature
- Siegfried Gottwald , Hans-Joachim Ilgauds and Karl-Heinz Schlote (ed.): Lexicon of important mathematicians . Verlag Harri Deutsch , Thun 1990, ISBN 3-8171-1164-9 , p. 482 ( MR1089881 ).
- Franz Xaver Mayer : Eduard Warings Meditationes algebraicae . Inaugural dissertation ( University of Zurich ). Überlingen (Lake Constance) 1923 ( WorldCat-Link ).
Remarks
- ↑ The article in the lexicon of important mathematicians (p. 482) draws on the above-mentioned dissertation by Franz Xaver Mayer.
- ↑ Here - as usual - stands for the associated derivative function , which is also a real polynomial function.