%0 Journal Article
%T Analytic Theory of Finite Asymptotic  Expansions in the Real Domain. Part II-B: Solutions of Differential Inequalities and Asymptotic Admissibility of Standard  Derivatives
%A Antonio Granata
%J Advances in Pure Mathematics
%P 481-502
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.58046
%X Part II-B of our work continues the factorizational theory of asymptotic expansions of type (*) <img src=\"Edit_34c23120-1a10-4ef2-a7ad-9f105e45eb2c.bmp\" width=\"0\" height=\"0\" alt=\"\" /><img src=\"Edit_34f50a58-8e29-4ffd-b25c-f9d86242b23e.bmp\" alt=\"\" />,<img src=\"Edit_9cf4c19d-0f92-47d4-857c-406c43b5785f.bmp\" alt=\"\" /> , <img src=\"Edit_cc483ab0-ea92-4a6f-a0e3-24e1754e2ab3.bmp\" alt=\"\" /> where the asymptotic scale <img src=\"Edit_a1781a95-df7b-4e2b-a9a0-50f43e560200.bmp\" alt=\"\" />, <img src=\"Edit_3f206227-400b-4e16-a3cb-5b3118ebc958.bmp\" alt=\"\" /> , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x<sub>0</sub>. The main result states that to each scale of this type it remains as-sociated an important class of functions (namely that of generalized convex functions) enjoying the property that the expansion (*), if valid, is automatically formally differentiable n ? 1 times in the two special senses characterized in Part II-A. A second result shows that formal applications of ordinary derivatives to an asymptotic expansion are rarely admissible and that they may also yield skew results even for scales of powers.
%K Asymptotic Expansions
%K Formal Differentiation of Asymptotic Expansions
%K Factorizations of  Ordinary Differential Operators
%K Chebyshev Asymptotic Scales
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=57681