Markov’s inequality in the o-minimal structure of convergent generalized power series
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Rafał Pierzchała
Abstract
We prove that the UPC (uniformly polynomially cuspidal) condition holds in an ominimal structure generated by some convergent generalized power series. The result is obtained by geometric and analytic methods. We get automatically some consequences. First of all, we obtain a new large class of sets with cusps satisfying Markov’s inequality (the class is strictly larger than the class of compact, fat and globally subanalytic sets). It may be useful from the point of view of approximation theory (multivariate polynomial inequalities) and constructive function theory. Our main result finds also practical application in complex analysis - it gives new examples of sets with the HCP property (Hölder continuity property of the Siciak extremal function).
© 2012 by Walter de Gruyter GmbH & Co.
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- Masthead
- Barycenters in Alexandrov spaces of curvature bounded below
- Isoperimetric problems in sectors with density
- Around A. D. Alexandrov’s uniqueness theorem for convex polytopes
- A relative isoperimetric inequality for certain warped product spaces
- Markov’s inequality in the o-minimal structure of convergent generalized power series
- Minimal area conics in the elliptic plane
- Geometry of semi-tube domains in ℂ2
- Flag transitive c:F4(2)-geometries
- Majorana representations of L3(2)
- A characterization of multiple (n – k)-blocking sets in projective spaces of square order
Articles in the same Issue
- Masthead
- Barycenters in Alexandrov spaces of curvature bounded below
- Isoperimetric problems in sectors with density
- Around A. D. Alexandrov’s uniqueness theorem for convex polytopes
- A relative isoperimetric inequality for certain warped product spaces
- Markov’s inequality in the o-minimal structure of convergent generalized power series
- Minimal area conics in the elliptic plane
- Geometry of semi-tube domains in ℂ2
- Flag transitive c:F4(2)-geometries
- Majorana representations of L3(2)
- A characterization of multiple (n – k)-blocking sets in projective spaces of square order
