%0 Journal Article
%T Analytic Theory of Finite Asymptotic  Expansions in the Real Domain. Part II-A:  The Factorizational Theory for Chebyshev Asymptotic Scales
%A Antonio Granata
%J Advances in Pure Mathematics
%P 454-480
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.58045
%X This paper, divided into three parts (Part II-A, Part II-B and Part II-C), contains the detailed factorizational theory of asymptotic expansions of type (?)&nbsp;<img src=\"Edit_7ed69a58-0a7b-4abc-8b31-c421d8d6c382.bmp\" alt=\"\" />, <img src=\"Edit_6e019ff7-189a-4c15-bfaf-14c29e60eb73.bmp\" alt=\"\" />, <img src=\"Edit_0400c81d-67b1-4d19-a443-a14118ad5049.bmp\" alt=\"\" />, where the asymptotic scale&nbsp;<img src=\"Edit_f625bef0-d631-414e-97bb-cd96dac22189.bmp\" alt=\"\" />, <img src=\"Edit_b20f571a-3400-41c9-be81-c013d9b9ab70.bmp\" alt=\"\" />, is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of  . It follows two pre-viously published papers: the first, labelled as Part I, contains the complete (elementary but non-trivial) theory for <img src=\"Edit_7fcc1f94-c2ba-486f-a87d-1adcadc2f738.bmp\" alt=\"\" />; the second is a survey highlighting only the main results without proofs. All the material appearing in ¡ì2 of the survey is here reproduced in an expanded form, as it contains all the preliminary formulas necessary to understand and prove the results. The remaining part of the survey¡ªespecially the heuristical considerations and consequent conjectures in ¡ì3¡ªmay serve as a good introduction to the complete theory.
%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=57680