Extending Tamm's theorem
Annales de l'Institut Fourier, Volume 44 (1994) no. 5, p. 1367-1395

We extend a result of M. Tamm as follows:

Let f:A,A m+n , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions xx r :(0,),r. Then there exists N such that for all (a,b)A, if yf(a,y) is C N in a neighborhood of b, then yf(a,y) is real analytic in a neighborhood of b.

On généralise un résultat de M. Tamm :

Soit f:A, A m+n , définissable dans le corps ordonné des nombres réels augmenté par toutes les fonctions analytiques réelles sur les cubes compacts et toutes les puissances xx r :(0,), r. Alors, il existe N telle que pour chaque (a,b)A, la fonction yf(a,y) est C N dans un voisinage de b si et seulement si yf(a,y) est analytique dans un voisinage de b.

@article{AIF_1994__44_5_1367_0,
     author = {Dries, Lou van den and Miller, Chris},
     title = {Extending Tamm's theorem},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {44},
     number = {5},
     year = {1994},
     pages = {1367-1395},
     doi = {10.5802/aif.1438},
     zbl = {0816.32004},
     mrnumber = {96g:32016},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1994__44_5_1367_0}
}
Dries, Lou van den; Miller, Chris. Extending Tamm's theorem. Annales de l'Institut Fourier, Volume 44 (1994) no. 5, pp. 1367-1395. doi : 10.5802/aif.1438. http://www.numdam.org/item/AIF_1994__44_5_1367_0/

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