Boundary values of functions in Cegrell’s class
Pham Hoang Hiep (2007)
Annales Polonici Mathematici
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We study boundary values of functions in Cegrell’s class .
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Pham Hoang Hiep (2007)
Annales Polonici Mathematici
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We study boundary values of functions in Cegrell’s class .
Eve Oja, Silja Treialt (2013)
Studia Mathematica
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The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair has the λ-bounded approximation property. Then there exists a net of finite-rank operators on X such that and for all α, and and converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
J. A. Nitsche (1975)
Publications mathématiques et informatique de Rennes
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Carsten Elsner (2006)
Colloquium Mathematicae
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We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function can be approximated with arbitrary accuracy by an infinite sum of analytic functions , each solving the same system of universal partial differential equations, namely (σ = 1,..., s).
Leetsch C. Hsu (1959)
Czechoslovak Mathematical Journal
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Per Åhag, Rafał Czyż, Pham Hoàng Hiêp (2007)
Annales Polonici Mathematici
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The energy class is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of and its pluricomplex p-energy is proved.
Damien Roy (2013)
Annales de l’institut Fourier
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A point with coordinates in a subfield of of transcendence degree one over , with linearly independent over , may have a uniform exponent of approximation by elements of that is strictly larger than the lower bound given by Dirichlet’s box principle. This appeared as a surprise, in connection to work of Davenport and Schmidt, for points of the parabola . The goal of this paper is to show that this phenomenon extends to all real conics defined over , and that the largest...
B. N. Rachajsky (1969)
Matematički Vesnik
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Slimane Benelkourchi, Vincent Guedj, Ahmed Zeriahi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Let be a compact Kähler manifold and be a smooth closed form of bidegree which is nonnegative and big. We study the classes of -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class . This is done by...
Svobodová, Ivona
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We consider functionals of a potential energy corresponding to . We are dealing with with . Various types of the subsoil of the plate are described by various types of the nonlinear term . The aim of the paper is to find a suitable computational algorithm.
A. Szankowski (2009)
Journal of the European Mathematical Society
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It is shown that there is a subspace of for which is isomorphic to such that does not have the approximation property. On the other hand, for there is a subspace of such that does not have the approximation property (AP) but the quotient space is isomorphic to . The result is obtained by defining random “Enflo-Davie spaces” which with full probability fail AP for all and have AP for all . For , are isomorphic to .
Yann Bugeaud (2015)
Acta Arithmetica
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Let d be a positive integer and α a real algebraic number of degree d + 1. Set . It is well-known that , where ||·|| denotes the distance to the nearest integer. Furthermore, for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that for any integer n ≥ 1.
Włodzimierz Łenski, Bogdan Roszak (2011)
Banach Center Publications
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We present an estimation of the and means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.
Yann Bugeaud (2014)
Publications mathématiques de Besançon
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The Littlewood conjecture in Diophantine approximation claims that holds for all real numbers and , where denotes the distance to the nearest integer. Its -adic analogue, formulated by de Mathan and Teulié in 2004, asserts that holds for every real number and every prime number , where denotes the -adic absolute value normalized by . We survey the known results on these conjectures and highlight recent developments. ...
Simon Baker (2015)
Acta Arithmetica
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Let β ∈ (1,2) and x ∈ [0,1/(β-1)]. We call a sequence a β-expansion for x if . We call a finite sequence an n-prefix for x if it can be extended to form a β-expansion of x. In this paper we study how good an approximation is provided by the set of n-prefixes. Given , we introduce the following subset of ℝ: In other words, is the set of x ∈ ℝ for which there exist infinitely many solutions to the inequalities . When , the Borel-Cantelli lemma tells us that the Lebesgue measure...
Urban Cegrell (2007)
Annales Polonici Mathematici
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We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
Jean-Pierre Demailly, Sławomir Dinew, Vincent Guedj, Pham Hoang Hiep, Sławomir Kołodziej, Ahmed Zeriahi (2014)
Journal of the European Mathematical Society
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Let be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on with right hand side, . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range of the complex Monge-Ampère operator acting on -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with -density belong to and proving that...
S. V. Konyagin, V. N. Temlyakov (2003)
Studia Mathematica
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We study the following nonlinear method of approximation by trigonometric polynomials. For a periodic function f we take as an approximant a trigonometric polynomial of the form , where is a set of cardinality m containing the indices of the m largest (in absolute value) Fourier coefficients f̂(k) of the function f. Note that Gₘ(f) gives the best m-term approximant in the L₂-norm, and therefore, for each f ∈ L₂, ||f-Gₘ(f)||₂ → 0 as m → ∞. It is known from previous results that in...
Takao Komatsu (2002)
Bulletin de la Société Mathématique de France
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Let be irrational. Several authors studied the numbers where is a positive integer and denotes the set of all real numbers of the form with restricted integer coefficients . The value of was determined for many particular Pisot numbers and for the golden number. In this paper the value of is determined for irrational numbers , satisfying with a positive integer .