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Granata, A. (2015) Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-B: Solutions of Differential Inequalities and Asymptotic Admissibility of Standard Derivatives. Advances in Pure Mathematics, 5, 481- 502.

has been cited by the following article:

• TITLE: Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part II-C: Constructive Algorithms for Canonical Factorizations and a Special Class of Asymptotic Scales

  AUTHORS: Antonio Granata

  KEYWORDS: Asymptotic Expansions, Canonical Factorizations of Disconjugate Operators, Algorithms for Canonical Factorizations, Chebyshev Asymptotic Scales

  JOURNAL NAME: Advances in Pure Mathematics, Vol.5 No.8, June 30, 2015

  ABSTRACT: This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.