Page 1

Displaying 1 – 16 of 16

Showing per page

Markov inequality on sets with polynomial parametrization

Mirosław Baran (1994)

Annales Polonici Mathematici

The main result of this paper is the following: if a compact subset E of n is UPC in the direction of a vector v S n - 1 then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].

Markov's property for kth derivative

Mirosław Baran, Beata Milówka, Paweł Ozorka (2012)

Annales Polonici Mathematici

Consider the normed space ( ( N ) , | | · | | ) of all polynomials of N complex variables, where || || a norm is such that the mapping L g : ( ( N ) , | | · | | ) f g f ( ( N ) , | | · | | ) is continuous, with g being a fixed polynomial. It is shown that the Markov type inequality | / z j P | | M ( d e g P ) m | | P | | , j = 1,...,N, P ( N ) , with positive constants M and m is equivalent to the inequality | | N / z . . . z N P | | M ' ( d e g P ) m ' | | P | | , P ( N ) , with some positive constants M’ and m’. A similar equivalence result is obtained for derivatives of a fixed order k ≥ 2, which can be more specifically formulated in the language of normed algebras. In...

Matrix inequalities and the complex Monge-Ampère operator

Jonas Wiklund (2004)

Annales Polonici Mathematici

We study two known theorems regarding Hermitian matrices: Bellman's principle and Hadamard's theorem. Then we apply them to problems for the complex Monge-Ampère operator. We use Bellman's principle and the theory for plurisubharmonic functions of finite energy to prove a version of subadditivity for the complex Monge-Ampère operator. Then we show how Hadamard's theorem can be extended to polyradial plurisubharmonic functions.

Maximal subextensions of plurisubharmonic functions

U. Cegrell, S. Kołodziej, A. Zeriahi (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

In our earlier paper [CKZ], we proved that any plurisubharmonic function on a bounded hyperconvex domain in n with zero boundary values in a quite general sense, admits a plurisubharmonic subextension to a larger hyperconvex domain. Here we study important properties of its maximal subextension and give informations on its Monge-Ampère measure. More generally, given a quasi-plurisubharmonic function ϕ on a given quasi-hyperconvex domain D X of a compact Kähler manifold ( X , ω ) , with well defined Monge-Ampère...

Meilleure approximation polynomiale et croissance des fonctions entières sur certaines variétés algébriques affines

Ahmed Zeriahi (1987)

Annales de l'institut Fourier

Soit K un compact polynomialement convexe de C n et V K son “potentiel logarithmique extrémal” dans C n . Supposons que K est régulier (i.e. V K continue) et soit f une fonction holomorphe sur un voisinage de K . On construit alors une suite { P } 1 de polynôme de n variables complexes avec deg ( P ) pour 1 , telle que l’erreur d’approximation max z K | f ( z ) - P ( z ) | soit contrôlée de façon assez précise en fonction du “pseudorayon de convergence” de f par rapport à K et du degré de convergence . Ce résultat est ensuite utilisé pour étendre...

Mesures de Mahler et équidistribution logarithmique

Antoine Chambert-Loir, Amaury Thuillier (2009)

Annales de l’institut Fourier

Soit X un schéma projectif intègre défini sur un corps de nombres  F  ; soit L un fibré en droites ample sur  X muni d’une métrique adélique semi-positive au sens de Zhang. Les résultats principaux de cet article sont :(1)Une formule qui calcule les hauteurs locales (relativement à  L ) d’un diviseur de Cartier sur  X comme des « mesures de Mahler » généralisées, c’est-à-dire les intégrales de fonctions de Green pour  D contre des mesures associées à  L  ;(2)Un théorème d’équidistribution des points de « petite »...

Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

Frédéric Campana, Henri Guenancia, Mihai Păun (2013)

Annales scientifiques de l'École Normale Supérieure

We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.

Monge-Ampère boundary measures

Urban Cegrell, Berit Kemppe (2009)

Annales Polonici Mathematici

We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.

Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods

W. Pleśniak (2006)

Banach Center Publications

We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces...

Currently displaying 1 – 16 of 16

Page 1