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Glaeser's continuity theorem : ウィキペディア英語版 | Glaeser's continuity theorem In mathematical analysis, Glaeser's continuity theorem, is a characterization of the continuity of the derivative of the square roots of functions of class . It was introduced in 1963 by Georges Glaeser,〔G. Glaeser, "Racine carrée d'une fonction différentiable", ''Ann. Inst. Fourier'' 13, no 2 (1963), 203–210 : (article )〕 and was later simplified by Jean Dieudonné.〔J. Dieudonné, "Sur un théorème de Glaeser", ''J. Analyse math.'' 23 (1970), 85–88 : (Résumé Zbl ), (article p.85 ), (article p.86 ), (article p.87 ) (the p. 88, not shown on the free preview contains the reference to Glaeser)〕 The theorem states: Let be a function of class in an open set ''U'' contained in , then is of class in ''U'' if and only if its partial derivatives of first and second order vanish in the zeros of ''f''. ==References==
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