Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-A: The Factorizational Theory for Chebyshev Asymptotic Scales

Antonio  Granata

doi:10.4236/apm.2015.58045

APM Vol.5 No.8 , June 2015

Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-A: The Factorizational Theory for Chebyshev Asymptotic Scales

Antonio Granata^*

Abstract: 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 (?) , , , where the asymptotic scale , , 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 ; the second is a survey highlighting only the main results without proofs. All the material appearing in §2 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—especially the heuristical considerations and consequent conjectures in §3—may serve as a good introduction to the complete theory.

Keywords: Asymptotic Expansions, Formal Differentiation of Asymptotic Expansions, Factorizations of Ordinary Differential Operators, Chebyshev Asymptotic Scales

Cite this paper: Granata, A. (2015) Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-A: The Factorizational Theory for Chebyshev Asymptotic Scales. Advances in Pure Mathematics, 5, 454-480. doi: 10.4236/apm.2015.58045.

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