Differentiability properties of log-analytic functions

DOI10.1216/rmj.2022.52.1423OpenAlexW3040527274MaRDI QIDQ2080687

Tobias Kaiser, Andre Opris

Publication date: 10 October 2022

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.03332

zbMATH Keywords

differentiabilitypreparation theoremlog-analytic functionsTamm's theorem

Mathematics Subject Classification ID

Real-analytic and semi-analytic sets (14P15) (C^infty)-functions, quasi-analytic functions (26E10) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Elementary functions (26A09) Real-analytic functions (26E05) Model theory of ordered structures; o-minimality (03C64)

Related Items (4)

Restricted log-exp-analytic power functions ⋮ Growth of log-analytic functions ⋮ On preparation theorems for R_{an, exp}-definable functions ⋮ Restricted log-exp-analytic functions and some differentiability results

Cites Work

• Integration of semialgebraic functions and integrated Nash functions
• Stability under integration of sums of products of real globally subanalytic functions and their logarithms
• Subanalytic sets in the calculus of variation
• Intégration des fonctions sous-analytiques et volumes des sous-ensembles sous-analytiques. (Integration of subanalytic functions and volumes of subanalytic subspaces)
• The elementary theory of restricted analytic fields with exponentiation
• Théorème de préparation pour les fonctions logarithmico-exponentielles. (Preparation theorem for logarithmico-exponential functions)
• Topologically Noetherian analytic algebras. Khovanskij's theory
• Extending Tamm's theorem
• Geometric categories and o-minimal structures
• A remark on the Lion-Rolin Preparation Theorem for LA-functions
• Infinite Differentiability in Polynomially Bounded O-Minimal Structures
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