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

Antonio Granata^{*}

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References

[1] Granata, A. (2011) Analytic Theory of Finite Asymptotic Expansions in the Real Domain. Part I: Two-Term Expansions of Differentiable Functions. Analysis Mathematica, 37, 245-287.

http://dx.doi.org/10.1007/s10476-011-0402-7

[2] Granata, A. (2007) Polynomial Asymptotic Expansions in the Real Domain: The Geometric, the Factorizational, and the Stabilization Approaches. Analysis Mathematica, 33, 161-198.

http://dx.doi.org/10.1007/s10476-007-0301-0

[3] Granata, A. (2010) The Problem of Differentiating an Asymptotic Expansion in Real Powers. Part I: Unsatisfactory or Partial Results by Classical Approaches. Analysis Mathematica, 36, 85-112.

http://dx.doi.org/10.1007/s10476-010-0201-6

[4] Granata, A. (2010) The Problem of Differentiating an Asymptotic Expansion in Real Powers. Part II: Factorizational Theory. Analysis Mathematica, 36, 173-218.

http://dx.doi.org/10.1007/s10476-010-0301-3

[5] Granata, A. (2015) The Factorizational Theory of Finite Asymptotic Expansions in the Real Domain: A Survey of the Main Results. Advances in Pure Mathematics, 5, 1-20.

http://dx.doi.org/10.4236/apm.2015.51001

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[7] Levin, A.Yu. (1969) Non-Oscillation of Solutions of the Equation . Uspekhi Matematicheskikh Nauk, 24, 43-96; Russian Mathematical Surveys, 24, 43-99.

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[8] Coppel, W.A. (1971) Disconjugacy. Lecture Notes in Mathematics. Vol. 220, Springer-Verlag, Berlin.

[9] Trench, W.F. (1974) Canonical Forms and Principal Systems for General Disconjugate Equations. Transactions of the American Mathematical Society, 189, 319-327.

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[10] Granata, A. (1980) Canonical Factorizations of Disconjugate Differential Operators. SIAM Journal on Mathematical Analysis, 11, 160-172. http://dx.doi.org/10.1137/0511014

[11] Granata, A. (1988) Canonical Factorizations of Disconjugate Differential Operator-Part II. SIAM Journal on Mathematical Analysis, 19, 1162-1173. http://dx.doi.org/10.1137/0519081

[12] Karlin, S. and Studden, W. (1966) Tchebycheff Systems: With Applications in Analysis and Statistics. Interscience, New York.

[13] Mazure, M.L. (2011) Quasi Extended Chebyshev Spaces and Weight Functions. Numerische Mathematik, 118, 79-108. http://dx.doi.org/10.1007/s00211-010-0312-9

[14] Pólya, G. (1922) On the Mean-Value Theorem Corresponding to a Given Linear Homogeneous Differential Equations. Transactions of the American Mathematical Society, 24, 312-324.

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[15] Schoenberg, I.J. (1982) Two Applications of Approximate Differentiation Formulae: An Extremum Problem for Multiply Monotone Functions and the Differentiation of Asymptotic Expansions. Journal of Mathematical Analysis and Applications, 89, 251-261.

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