The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform
Ragnar Sigurdsson - One of the best experts on this subject based on the ideXlab platform.
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Relative Extremal Functions and characterization of pluripolar sets in complex manifolds
Transactions of the American Mathematical Society, 2010Co-Authors: Armen Edigarian, Ragnar SigurdssonAbstract:We study a disc formula for the relative Extremal Function for a subset of a complex manifold and apply it to give a description of pluripolar sets and polynomial hulls.
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SICIAK-ZAHARIUTA Extremal FunctionS, ANALYTIC DISCS AND POLYNOMIAL HULLS
Mathematische Annalen, 2009Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We prove two disc formulas for the Siciak–Zahariuta Extremal Function of an arbitrary open subset of complex affine space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex affine space in terms of analytic discs. Similar results in previous work of ours required the subsets to be connected.
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Siciak-Zahariuta Extremal Functions and polynomial hulls
arXiv: Complex Variables, 2007Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We use our disc formula for the Siciak-Zahariuta Extremal Function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.
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disc formulas for the weighted siciak zahariuta Extremal Function
arXiv: Complex Variables, 2006Co-Authors: Benedikt Steinar Magnusson, Ragnar SigurdssonAbstract:We prove a disc formula for the weighted Siciak-Zahariuta Extremal Function $V_{X,q}$ for an upper semicontinuous Function $q$ on an open connected subset $X$ in $\C^n$. This Function is also known as the weighted Green Function with logaritmic pole at infinity and weighted global Extremal Function.
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the relative Extremal Function for borel sets in complex manifolds
arXiv: Complex Variables, 2006Co-Authors: Armen Edigarian, Ragnar SigurdssonAbstract:We study a disc formula for the relative Extremal Function for Borel sets in complex manifolds.
Rafal Pierzchala - One of the best experts on this subject based on the ideXlab platform.
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an estimate for the siciak Extremal Function subanalytic geometry approach
Journal of Mathematical Analysis and Applications, 2015Co-Authors: Rafal PierzchalaAbstract:We study the Łojasiewicz–Siciak inequality in CN. This concerns the estimating from below the Siciak Extremal Function which is very much related to the Green Function in C. As an application we present some results describing how fast holomorphic Functions defined in a neighbourhood of a compact holomorphic polyhedron can be approximated uniformly on this polyhedron by complex polynomials.
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siciak s Extremal Function of non upc cusps i
Journal de Mathématiques Pures et Appliquées, 2010Co-Authors: Rafal PierzchalaAbstract:Abstract There are several criteria of L-regularity of compact sets in C N . One of the most important is the semianalytic accessibility criterion due to Pleśniak. We propose here a method that allows to prove L-regularity of some cusps for which the semianalytic accessibility criterion fails. We also prove a result connecting L-regularity with a question of Sadullaev. Moreover, we give some results concerning polynomial approximation of power Functions.
Francisco S B Albuquerque - One of the best experts on this subject based on the ideXlab platform.
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sharp constant and Extremal Function for weighted trudinger moser type inequalities in r2
Journal of Mathematical Analysis and Applications, 2015Co-Authors: Francisco S B AlbuquerqueAbstract:Abstract In this note, we prove the sharpness and the existence of Extremal Function for a Trudinger–Moser type inequality in weighted Sobolev spaces established by Albuquerque–Alves–Medeiros in 2014 (see [6, Theorem 1.1] ).
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Sharp constant and Extremal Function for weighted Trudinger–Moser type inequalities in R2
Journal of Mathematical Analysis and Applications, 2015Co-Authors: Francisco S B AlbuquerqueAbstract:Abstract In this note, we prove the sharpness and the existence of Extremal Function for a Trudinger–Moser type inequality in weighted Sobolev spaces established by Albuquerque–Alves–Medeiros in 2014 (see [6, Theorem 1.1] ).
Benedikt Steinar Magnusson - One of the best experts on this subject based on the ideXlab platform.
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Analytic discs, global Extremal Functions and projective hulls in projective space
Illinois Journal of Mathematics, 2014Co-Authors: Benedikt Steinar MagnussonAbstract:Using a recent result of Larusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global Extremal Function for domains in P n . As a corollary we get a characterization of the projective hull for connected compact sets in P n by the existence of analytic discs.
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Analytic Discs, Global Extremal Functions and Projective Hulls in Projective Space
arXiv: Complex Variables, 2013Co-Authors: Benedikt Steinar MagnussonAbstract:Using a recent result of L\'arusson and Poletsky regarding plurisubharmonic subextensions we prove a disc formula for the quasiplurisubharmonic global Extremal Function for domains in complex projective space. As a corollary we get a characterization of the projective hull for connected compact sets in complex projective space by the existence of analytic discs.
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disc formulas for the weighted siciak zahariuta Extremal Function
arXiv: Complex Variables, 2006Co-Authors: Benedikt Steinar Magnusson, Ragnar SigurdssonAbstract:We prove a disc formula for the weighted Siciak-Zahariuta Extremal Function $V_{X,q}$ for an upper semicontinuous Function $q$ on an open connected subset $X$ in $\C^n$. This Function is also known as the weighted Green Function with logaritmic pole at infinity and weighted global Extremal Function.
Finnur Larusson - One of the best experts on this subject based on the ideXlab platform.
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SICIAK-ZAHARIUTA Extremal FunctionS, ANALYTIC DISCS AND POLYNOMIAL HULLS
Mathematische Annalen, 2009Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We prove two disc formulas for the Siciak–Zahariuta Extremal Function of an arbitrary open subset of complex affine space. We use these formulas to characterize the polynomial hull of an arbitrary compact subset of complex affine space in terms of analytic discs. Similar results in previous work of ours required the subsets to be connected.
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Siciak-Zahariuta Extremal Functions and polynomial hulls
arXiv: Complex Variables, 2007Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We use our disc formula for the Siciak-Zahariuta Extremal Function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.
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the siciak zahariuta Extremal Function as the envelope of disc Functionals
arXiv: Complex Variables, 2005Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We establish disc formulas for the Siciak-Zahariuta Extremal Function of an arbitrary open subset of complex affine space, generalizing Lempert's formula for the convex case. This Function is also known as the pluricomplex Green Function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert's formula for this Function from the convex case to the connected case.
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the siciak zahariuta Extremal Function as the envelope of disc Functionals
Annales Polonici Mathematici, 2005Co-Authors: Finnur Larusson, Ragnar SigurdssonAbstract:We establish disc formulas for the Siciak-Zahariuta Extremal Function of an arbitrary open subset of complex affine space. This Function is also known as the pluricomplex Green Function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert’s formula for this Function from the convex case to the connected case. Introduction The Siciak-Zahariuta Extremal Function VX of a subset X of complex affine space C is defined as the supremum of all entire plurisubharmonic Functions u of minimal growth with u|X ≤ 0. It is also called the pluricomplex Green Function of X with logarithmic growth or a logarithmic pole at infinity (although this is a bit of a misnomer if X is not bounded). A plurisubharmonic Function u on C is said to have minimal growth (and belong to the class L) if u− log ‖·‖ is bounded above on C. If X is open and nonempty, then VX ∈ L. More generally, if X is not pluripolar, then the upper semicontinuous regularization V ∗ X of VX is in L, and if X is pluripolar, then V ∗ X =∞. Siciak-Zahariuta Extremal Functions play a fundamental role in pluripotential theory and have found important applications in approximation theory, complex dynamics, and elsewhere. For a detailed account of the basic theory, see [K, Chapter 5]. For an overview of some recent developments, see [Pl]. The Extremal Functions of pluripotential theory are usually defined as suprema of classes of plurisubharmonic Functions with appropriate properties. The theory of disc Functionals, initiated by Poletsky in the late 1980s [P1, PS], offers a different approach to Extremal Functions, realizing them as envelopes of disc Functionals. A disc Functional on a complex manifold Y is a map H into R = [−∞,∞] from the set of analytic discs in Y , that is, holomorphic maps from the open unit disc D into Y . We usually restrict ourselves to analytic discs that extend holomorphically to a neighbourhood of the closed unit disc. 2000 Mathematics Subject Classification. Primary: 32U35. The first-named author was supported in part by the Natural Sciences and Engineering Research Council of Canada. First version 22 April 2005. Second, expanded version 6 July 2005. Typeset by AMS-TEX 1 The envelope EH of H is the map Y → R that takes a point x ∈ Y to the infimum of the values H(f) for all analytic discs f in Y with f(0) = x. Disc formulas have been proved for such Extremal Functions as largest plurisubharmonic minorants, including relative Extremal Functions, and pluricomplex Green Functions of various sorts, and used to establish properties of these Functions that had proved difficult to handle via the supremum definition. Some of this work has been devoted to extending to arbitrary complex manifolds results that were first proved for domains in C. See for instance [BS, E, EP, LS1, LS2, LLS, P2, P3, R, RS]. In the convex case, there is a disc formula for the Siciak-Zahariuta Extremal Function due to Lempert [M, Appendix]. The main motivation for the present work was to generalize Lempert’s formula. Because of the growth condition in the definition of the Siciak-Zahariuta Extremal Function, we did not see how to fit it into the theory of disc Functionals until we realized, from a remark of Guedj and Zeriahi [GZ], that minimal growth is nothing but quasi-plurisubharmonicity with respect to the current of integration along the hyperplane at infinity. This observation is implicit in the proof of Theorem 1, which presents a family of new disc formulas for the Siciak-Zahariuta Extremal Function of an arbitrary open subset of affine space. Theorem 2 contains more such formulas. Our main result, Theorem 3, establishes Lempert’s formula, in the following slightly modified form, for every connected open subset of affine space. The formula is easily seen to fail for disconnected sets in general. Theorem. The Siciak-Zahariuta Extremal Function VX of a connected open subset X of C is given by the disc formula
