On subextension and approximation of plurisubharmonic functions with given boundary values

Hichame Amal

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Displaying similar documents to “On subextension and approximation of plurisubharmonic functions with given boundary values”

Boundary values of functions in Cegrell’s class $_{ψ}$

Pham Hoang Hiep (2007)

Annales Polonici Mathematici

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We study boundary values of functions in Cegrell’s class $_{ψ}$ .

Some duality results on bounded approximation properties of pairs

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 $(X *, Y^{⊥})$ has the λ-bounded approximation property. Then there exists a net $(S_{α})$ of finite-rank operators on X such that $S_{α} (Y) \subset Y$ and $| | S_{α} | | \leq λ$ for all α, and $(S_{α})$ and $(S *_{α})$ 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.

$L_{\infty}$ -Convergence of Finite Element Approximation

J. A. Nitsche (1975)

Publications mathématiques et informatique de Rennes

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On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

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 $f : ℝ^{s} \to ℝ$ can be approximated with arbitrary accuracy by an infinite sum $\sum_{r = 1}^{\infty} H_{r} (x ₁, . . ., x_{s}) \in C^{\infty} (ℝ^{s})$ of analytic functions $H_{r}$ , each solving the same system of universal partial differential equations, namely $P (x_{σ}; H_{r}, \partial H_{r} / \partial x_{σ}, . . ., \partial ⁵ H_{r} / \partial x ⁵_{σ} ⁵) = 0$ (σ = 1,..., s).

The polynomial approximation of continuous functions defined on $(- \infty, \infty)$

Leetsch C. Hsu (1959)

Czechoslovak Mathematical Journal

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Concerning the energy class $_{p}$ for 0 < p < 1

Per Åhag, Rafał Czyż, Pham Hoàng Hiêp (2007)

Annales Polonici Mathematici

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The energy class $_{p}$ is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of $ℱ_{p}$ and its pluricomplex p-energy is proved.

Routh-type $L_{2}$ model reduction revisited

Wiesław Krajewski, Umberto Viaro (2018)

Kybernetika

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A computationally simple method for generating reduced-order models that minimise the $L_{2}$ norm of the approximation error while preserving a number of second-order information indices as well as the steady-state value of the step response, is presented. The method exploits the energy-conservation property peculiar to the Routh reduction method and the interpolation property of the $L_{2}$ -optimal approximation. Two examples taken from the relevant literature show that the suggested techniques...

Rational approximation to real points on conics

Damien Roy (2013)

Annales de l’institut Fourier

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A point $(ξ_{1}, ξ_{2})$ with coordinates in a subfield of $ℝ$ of transcendence degree one over $ℚ$ , with $1, ξ_{1}, ξ_{2}$ linearly independent over $ℚ$ , may have a uniform exponent of approximation by elements of $ℚ^{2}$ that is strictly larger than the lower bound $1 / 2$ given by Dirichlet’s box principle. This appeared as a surprise, in connection to work of Davenport and Schmidt, for points of the parabola ${(ξ, ξ^{2}); ξ \in ℝ}$ . The goal of this paper is to show that this phenomenon extends to all real conics defined over $ℚ$ , and that the largest...

On the Monge-Ampere differential equation $r t - s^{2} + λ^{2} (x, y) = 0$

B. N. Rachajsky (1969)

Matematički Vesnik

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A priori estimates for weak solutions of complex Monge-Ampère equations

Slimane Benelkourchi, Vincent Guedj, Ahmed Zeriahi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X$ be a compact Kähler manifold and $ω$ be a smooth closed form of bidegree $(1, 1)$ which is nonnegative and big. We study the classes $ℰ_{χ} (X, ω)$ of $ω$ -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight $χ$ 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 $ℰ_{χ} (X, ω)$ . This is done by...

Numerical approximation of the non-linear fourth-order boundary-value problem

Svobodová, Ivona

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We consider functionals of a potential energy $ℙ_{ψ} (u)$ corresponding to $𝑎𝑛 𝑎𝑥𝑖𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 - 𝑣𝑎𝑙𝑢𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚$ . We are dealing with $𝑎 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎 𝑡ℎ𝑖𝑛 𝑎𝑛𝑛𝑢𝑙𝑎𝑟 𝑝𝑙𝑎𝑡𝑒$ with $𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠$ . Various types of the subsoil of the plate are described by various types of the $𝑛𝑜𝑛𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑏𝑙𝑒$ nonlinear term $ψ (u)$ . The aim of the paper is to find a suitable computational algorithm.

Three-space problems for the approximation property

A. Szankowski (2009)

Journal of the European Mathematical Society

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It is shown that there is a subspace $Z_{q}$ of $ℓ_{q}$ for $1 < q < 2$ which is isomorphic to $ℓ_{q}$ such that $ℓ_{q} / Z_{q}$ does not have the approximation property. On the other hand, for $2 < p < \infty$ there is a subspace $Y_{p}$ of $ℓ_{p}$ such that $Y_{p}$ does not have the approximation property (AP) but the quotient space $ℓ_{p} / Y_{p}$ is isomorphic to $ℓ_{p}$ . The result is obtained by defining random “Enflo-Davie spaces” $Y_{p}$ which with full probability fail AP for all $2 < p \leq \infty$ and have AP for all $1 \leq p \leq 2$ . For $1 < p \leq 2$ , $Y_{p}$ are isomorphic to $ℓ_{p}$ .

On the multiples of a badly approximable vector

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 $α ̲ : = (α, α ², . . ., α^{d})$ . It is well-known that $c (α ̲) : = l i m i n f_{q \to \infty} q^{1 / d} \cdot | | q α ̲ | | > 0$ , where ||·|| denotes the distance to the nearest integer. Furthermore, $c (α ̲) n^{- 1 / d} \leq c (n α ̲) \leq n c (α ̲)$ for any integer n ≥ 1. Our main result asserts that there exists a real number C, depending only on α, such that $c (n α ̲) \leq C n^{- 1 / d}$ for any integer n ≥ 1.

Lebesgue type points in strong (C,α) approximation of Fourier series

Włodzimierz Łenski, Bogdan Roszak (2011)

Banach Center Publications

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We present an estimation of the $H_{k ₀, k_{r}}^{q, α} f$ and $H_{λ, u}^{ϕ, α} f$ 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.