A comparison of two different ways to define classes of ultradifferentiable functions
Bonet, José ; Meise, Reinhold ; Melikhov, Sergej N.
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 425-444 / Harvested from Project Euclid
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We characterize the weight sequences $(M_p)_p$ such that the class of ultra-differentiable functions ${\mathcal E}_{(M_p)}$ defined by imposing conditions on the derivatives of the function in terms of this sequence coincides with a class of ultradifferentiable functions ${\mathcal E}_{(\omega)}$ defined by imposing conditions on the Fourier Laplace transform. As a corollary, we characterize the weight functions $\omega$ for which there exists a weight sequence $(M_p)_p$ such that the classes ${\mathcal E}_{(\omega)}$ and ${\mathcal E}_{(M_p)}$ coincide. These characterizations also hold in the Roumieu case. Our main results are illustrated by several examples.
Publié le : 2007-09-14
Classification:  
@article{1190994204,
     author = {Bonet, Jos\'e and Meise, Reinhold and Melikhov, Sergej N.},
     title = {A comparison of two different ways to define classes of ultradifferentiable functions},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 425-444},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1190994204}
}

Bonet, José; Meise, Reinhold; Melikhov, Sergej N. A comparison of two different ways to define classes of ultradifferentiable functions. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  425-444. http://gdmltest.u-ga.fr/item/1190994204/