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.