THE REAL FIELD WITH CONVERGENT GENERALIZED POWER SERIES

No abstract is available for this paper.

• Publication year

  1998

• Venue

  Transactions of the American Mathematical Society

• Publication date

  Unknown publication date

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1090/S0002-9947-98-02105-9
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Lectures on Riemann Surfaces

  1999influential reference
• Tame Topology and O-minimal Structures

  1998cited by this paper
• Logarithmic‐Exponential Power Series

  1997cited by this paper
• Geometric categories and o-minimal structures

  1996cited by this paper
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function

  1996cited by this paper
• Sur les ensembles semi-analytiques avec conditions Gevrey au bord

  1994influential reference
• Expansions of the Real Field with Power Functions

  1994cited by this paper
• The Elementary Theory of Restricted Analytic Fields with Exponentiation

  1994cited by this paper
• Semianalytic and subanalytic sets

  1988influential reference
• P-adic and real subanalytic sets

  1988cited by this paper
• Lie Algebras And Lie Groups

  1967cited by this paper
• Ensembles semi-analytiques

  1965cited by this paper
• Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen

  1953cited by this paper

• Subdifferentiation with symmetry

  2025cites this paper
• On the convergence of critical points on real algebraic sets and applications to optimization

  2025cites this paper
• Definability of complex functions in o-minimal structures

  2025cites this paper
• Quasianalytic algebras with weakly smooth germs generate o-minimal structures

  2025influential citation
• A quasianalytic class with weakly smooth germs

  2025influential citation
• Transasymptotic expansions of o-minimal germs

  2024influential citation
• Nondefinability results with entire functions of finite order in polynomially bounded o-minimal structures

  2024cites this paper
• The appeals of quadratic majorization–minimization

  2024cites this paper
• Computing positive tropical varieties and lower bounds on the number of positive roots

  2024cites this paper
• Signed Tropicalization of Polar Cones

  2023cites this paper
• Mellin transforms of power-constructible functions

  2023cites this paper
• Factorization of polynomials over the symmetrized tropical semiring and Descartes' rule of sign over ordered valued fields

  2023cites this paper
• Global convergence of the gradient method for functions definable in o-minimal structures

  2023influential citation
• Newton Polyhedra and Stratified Resolution of Singularities in the Class of Generalized Power Series

  2023cites this paper
• SIGNED TROPICALIZATION OF POLARS AND APPLICATION TO MATRIX CONES

  2023cites this paper
• AMALGAMATING THE REAL GAMMA AND ZETA FUNCTIONS

  2022cites this paper
• Multisummability for generalized power series

  2022influential citation
• HALFSPACES AND

  2022cites this paper
• Signed tropical halfspaces and convexity

  2022cites this paper
• Stratified reduction of singularities of generalized analytic functions

  2022influential citation
• What Tropical Geometry Tells Us about the Complexity of Linear Programming

  2021cites this paper
• The tropicalization of the entropic barrier

  2020cites this paper
• Tropical Spectrahedra

  2020cites this paper
• Tropical Ehrhart theory and tropical volume

  2019cites this paper
• On sample complexity of neural networks

  2019cites this paper
• On the Reeb Spaces of Definable Maps

  2018cites this paper
• Polyhedral Tropical Geometry of Higher Rank.

  2018cites this paper
• Condition numbers of stochastic mean payoff games and what they say about nonarchimedean semidefinite programming

  2018cites this paper
• Ilyashenko algebras based on transserial asymptotic expansions

  2018cites this paper
• Tropical totally positive matrices

  2018cites this paper
• Expansions of the Real Field by Canonical Products

  2018cites this paper
• Convergent Puiseux Series and Tropical Geometry of Higher Rank

  2018influential citation
• Spectraèdres tropicaux: application à la programmation semi-définie et aux jeux à paiement moyen. (Tropical spectrahedra: Application to semidefinite programming and mean payoff games)

  2018cites this paper
• Log-Barrier Interior Point Methods Are Not Strongly Polynomial

  2017cites this paper
• Tangent cones and $C^1$ regularity of definable sets

  2017cites this paper
• Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

  2016cites this paper
• Solving Generic Nonarchimedean Semidefinite Programs Using Stochastic Game Algorithms

  2016cites this paper
• Tameness in expansions of the real field

  2016cites this paper
• Tropical Spectrahedra

  2016cites this paper
• Tropical totally positive matrices

  2016cites this paper
• Quasianalytic Ilyashenko Algebras

  2016cites this paper
• Descent dynamical systems and algorithms for tame optimization, and multi-objective problems. (Systèmes dynamiques de descente et algorithmes pour l'optimisation modérée, et les problèmes multi-objectif)

  2015cites this paper
• Tropical methods for the localization of eigenvalues and application to their numerical computation

  2015cites this paper
• MULTIVARIABLE NEWTON-PUISEUX THEOREM FOR GENERALISED QUASIANALYTIC

  2015cites this paper
• Remez-type inequality on sets with cusps

  2015cites this paper
• Definable obstruction theory

  2014cites this paper
• Long and winding central paths

  2014cites this paper
• A definable Borsuk-Ulam type theorem

  2014cites this paper
• Approximation of o-minimal maps satisfying a Lipschitz condition

  2014cites this paper
• Tropical aspects of linear programming

  2014cites this paper
• On smooth locally o-minimal functions

  2014cites this paper
• Local monomialization of generalized analytic functions

  2013cites this paper
• Definable Zero-Sum Stochastic Games

  2013cites this paper
• Multivariable Newton-Puiseux Theorem for Generalised Quasianalytic Classes

  2013cites this paper
• Real algebraic geometry

  2013cites this paper
• Multivariable Newton-Puiseux Theorem for Convergent Generalised Power Series

  2013cites this paper
• Quantifier elimination and rectilinearization theorem for generalized quasianalytic algebras

  2013cites this paper
• Hausdorff limits of Rolle leaves

  2012cites this paper
• On generalized series fields and exponential-logarithmic series fields with derivations

  2012cites this paper
• On fields of totally $\mathfrak{S}$-adic numbers. With an appendix by Florian Pop

  2012cites this paper
• DOCTEUR DE L'ÉCOLE POLYTECHNIQUE

  2012cites this paper
• Valuation theory of exponential Hardy fields II: Principal parts of germs in the Hardy field of o-minimal exponential expansions of the reals

  2012cites this paper
• Construction of O-minimal Structures from Quasianalytic Classes

  2012cites this paper
• Basics of O-minimality and Hardy Fields

  2012cites this paper
• J un 2 01 2 Valuation theory of exponential Hardy fields ∗

  2012cites this paper
• Local monomialization of generalized analytic functions

  2012influential citation
• Hausdorff limits of Rolle leaves

  2011cites this paper
• JOHN FUNCTIONS FOR o-MINIMAL DOMAINS

  2011cites this paper
• Mildness and the Density of Rational Points on Certain Transcendental Curves

  2011cites this paper
• Harmonic measure and subanalytically tame measures

  2010cites this paper
• Differential Dynamic Logic dℒ

  2010cites this paper
• Characterizing decidability in a quasianalytic setting

  2010cites this paper
• Sheaves on T-topologies

  2010cites this paper
• Peano differentiable extensions in o-minimal structures

  2010cites this paper
• Singularities of o‐minimal Peano derivatives

  2010cites this paper
• Siciak's extremal function of non-UPC cusps. I

  2010cites this paper
• Maps on Ultrametric Spaces, Hensel's Lemma, and Differential Equations Over Valued Fields

  2010cites this paper
• Action de derivations irreductibles sur les algebres quasi-regulieres d'Hilbert

  2009cites this paper
• DEFINABLE C∞G MANIFOLD STRUCTURES OF DEFINABLE CG MANIFOLDS

  2009cites this paper
• O-minimal Analytic Separation of Sets in Dimension 2

  2009cites this paper
• An o-minimal structure which does not admit $C^{\infty }$ cellular decomposition

  2009cites this paper
• THE SMITH HOMOLOGY AND BORSUK-ULAM TYPE THEOREMS

  2009cites this paper
• Decomposition into special cubes and its applications to quasi-subanalytic geometry

  2009cites this paper
• Cell decomposition and dimension function in the theory of closed ordered differential fields

  2009cites this paper
• A GENERALIZED BORSUK-ULAM THEOREM IN A REAL CLOSED FIELD

  2009cites this paper
• ALGEBRAIC MODELS FOR O-MINIMAL MANIFOLDS

  2008cites this paper
• DEFINABLE C r FIBER BUNDLES AND DEFINABLE C r G VECTOR BUNDLES

  2008cites this paper
• Comparison theorems for o-minimal singular (co)homology

  2008cites this paper
• Locally definable fiber bundles

  2008cites this paper
• Géométrie analytique Une structure o-minimale sans décomposition cellulaire C ∞

  2008cites this paper
• Relative properties of definable C ∞ manifolds with finite abelian group actions in an o-minimal expansion of R exp

  2008cites this paper
• Zero-set property of $o$-minimal indefinitely Peano differentiable functions

  2008cites this paper
• Smooth functions in o-minimal structures

  2008cites this paper
• THE RIEMANN MAPPING THEOREM FOR o-MINIMAL FUNCTIONS

  2008cites this paper
• RELATIVE DEFINABLE CG TRIVIALITY OF G INVARIANT PROPER DEFINABLE C FUNCTIONS

  2008cites this paper
• DEFINABLE SMOOTHING OF LIPSCHITZ CONTINUOUS FUNCTIONS

  2008cites this paper
• Corso di Perfezionamento in Matematica

  2007cites this paper
• o-MINIMAL ČECH COHOMOLOGY

  2007cites this paper
• The Riemann mapping theorem for semianalytic domains and o‐minimality

  2007cites this paper
• Extending o-minimal Fréchet derivatives

  2007cites this paper