Growth Properties of Functions in Hardy Fields

DOI10.2307/2000493zbMath0619.34057OpenAlexW4236193724MaRDI QIDQ3755816

Maxwell Rosenlicht

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000493

zbMATH Keywords

Hardy fieldsrates of growthlogarithmic-exponential functions

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Algebraic numbers; rings of algebraic integers (11R04) Asymptotic expansions of solutions to ordinary differential equations (34E05)

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Uniform distribution and Hardy fields ⋮ Book review of: M. Aschenbrenner et al., Asymptotic differential algebra and model theory of transseries ⋮ Addendum: Growth orders occurring in expansions of Hardy-field solutions of algebraic differential equations ⋮ Asymptotics in a Hardy field ⋮ Unnamed Item ⋮ Surreal numbers with derivation, Hardy fields and transseries: a survey ⋮ Basics of O-minimality and Hardy Fields ⋮ Non-oscillating solutions of a differential equation and Hardy fields ⋮ Transseries as germs of surreal functions ⋮ Linear independence of finite Gabor systems determined by behavior at infinity ⋮ Logarithmic-exponential series ⋮ Rosenlicht Fields ⋮ Avoiding the projective hierarchy in expansions of the real field by sequences ⋮ Primary decomposition of lattice basis ideals ⋮ Fractional iteration of series and transseries ⋮ Symbolic asymptotics: Multiseries of inverse functions ⋮ Growth estimates for exp-log functions ⋮ Comparison of exponential-logarithmic and logarithmic-exponential series ⋮ Differential equations over polynomially bounded o-minimal structures

Cites Work

• New orders of infinity
• Hardy fields and existence of transexponential functions
• The Rank of a Hardy Field
• Rank change on adjoining real powers to Hardy fields