Abstract
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.
Citation
José Bonet. Reinhold Meise. Sergej N. Melikhov. "A comparison of two different ways to define classes of ultradifferentiable functions." Bull. Belg. Math. Soc. Simon Stevin 14 (3) 425 - 444, September 2007. https://doi.org/10.36045/bbms/1190994204
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