On generalized definitions of ultradifferentiable classes
Functional Analysis
2023-06-05 v2 Classical Analysis and ODEs
Abstract
We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipovi\'c, N. Teofanov and F. Tomi\'c are special cases of the general framework of spaces of ultradifferentiable functions defined in terms of weight matrices in the sense of A. Rainer and the third author. We study classes "beyond geometric growth factors" defined in terms of a weight sequence and an exponent sequence, prove that these new types admit a weight matrix representation and transfer known results from the matrix-type to such a non-standard ultradifferentiable setting.
Cite
@article{arxiv.2211.08090,
title = {On generalized definitions of ultradifferentiable classes},
author = {Javier Jiménez-Garrido and David Nicolas Nenning and Gerhard Schindl},
journal= {arXiv preprint arXiv:2211.08090},
year = {2023}
}
Comments
Some typos corrected; to appear in Journal of Mathematical Analysis and Applications