Wiener's type regularity criteria on the complex plane

Józef Siciak

Displaying similar documents to “Wiener's type regularity criteria on the complex plane”

On Dirichlet type spaces on the unit ball of $ℂ^{n}$

Małgorzata Michalska (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we discuss characterizations of Dirichlet type spaces on the unit ball of $ℂ^{n}$ obtained by P. Hu and W. Zhang [2], and S. Li [4].

On the Dirichlet problem associated with the Dunkl Laplacian

Mohamed Ben Chrouda (2016)

Annales Polonici Mathematici

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This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian $Δ_{k}$ as well as the hypoellipticity of $Δ_{k}$ on noninvariant open sets.

The Dirichlet-Bohr radius

Daniel Carando, Andreas Defant, Domingo A. Garcí, Manuel Maestre, Pablo Sevilla-Peris (2015)

Acta Arithmetica

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Denote by Ω(n) the number of prime divisors of n ∈ ℕ (counted with multiplicities). For x∈ ℕ define the Dirichlet-Bohr radius L(x) to be the best r > 0 such that for every finite Dirichlet polynomial $\sum_{n \leq x} a_{n} n^{- s}$ we have $\sum_{n \leq x} | a_{n} | r^{Ω (n)} \leq s u p_{t \in ℝ} | \sum_{n \leq x} a_{n} n^{- i t} |$ . We prove that the asymptotically correct order of L(x) is ${(l o g x)}^{1 / 4} x^{- 1 / 8}$ . Following Bohr’s vision our proof links the estimation of L(x) with classical Bohr radii for holomorphic functions in several variables. Moreover, we suggest a general setting which allows translating various results...

The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian, B. Calado, H. Queffélec (2006)

Studia Mathematica

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We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if $f (s) = \sum_{n = 1}^{\infty} a ₙ n^{- s}$ with ${| | f | |}_{\infty} : = s u p_{ℜ s > 0} | f (s) | < \infty$ , then $\sum_{n = 1}^{\infty} | a ₙ | n^{- 2} {\leq | | f | |}_{\infty}$ and even slightly better, and $\sum_{n = 1}^{\infty} | a ₙ | n^{- 1 / 2} {\leq C | | f | |}_{\infty}$ , C being an absolute constant.

Inequalities for a regular polygon in $L^{p}$ spaces

M. Pavlović (1992)

Matematički Vesnik

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On the Dirichlet problem in the Cegrell classes

Rafał Czyż, Per Åhag (2004)

Annales Polonici Mathematici

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Let μ be a non-negative measure with finite mass given by $φ (d d^{c} ψ) ⁿ$ , where ψ is a bounded plurisubharmonic function with zero boundary values and $φ \in L^{q} ((d d^{c} ψ) ⁿ)$ , φ ≥ 0, 1 ≤ q ≤ ∞. The Dirichlet problem for the complex Monge-Ampère operator with the measure μ is studied.

Admissible functions for the Dirichlet space

Javad Mashreghi, Mahmood Shabankhah (2010)

Studia Mathematica

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Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of $^{\infty}$ .

The comparison principle and Dirichlet problem in the class $_{p} (f)$ , p > 0

Pham Hoang Hiep (2006)

Annales Polonici Mathematici

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We establish the comparison principle in the class $_{p} (f)$ . The result obtained is applied to the Dirichlet problem in $_{p} (f)$ .

Regularity of certain sets in ℂⁿ

Nguyen Quang Dieu (2003)

Annales Polonici Mathematici

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A subset K of ℂⁿ is said to be regular in the sense of pluripotential theory if the pluricomplex Green function (or Siciak extremal function) $V_{K}$ is continuous in ℂⁿ. We show that K is regular if the intersections of K with sufficiently many complex lines are regular (as subsets of ℂ). A complete characterization of regularity for Reinhardt sets is also given.

IP-Dirichlet measures and IP-rigid dynamical systems: an approach via generalized Riesz products

Sophie Grivaux (2013)

Studia Mathematica

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If ${(n_{k})}_{k \geq 1}$ is a strictly increasing sequence of integers, a continuous probability measure σ on the unit circle is said to be IP-Dirichlet with respect to ${(n_{k})}_{k \geq 1}$ if $σ ̂ (\sum_{k \in F} n_{k}) \to 1$ as F runs over all non-empty finite subsets F of ℕ and the minimum of F tends to infinity. IP-Dirichlet measures and their connections with IP-rigid dynamical systems have recently been investigated by Aaronson, Hosseini and Lemańczyk. We simplify and generalize some of their results, using an approach involving generalized Riesz...

Dirichlet forms on quotients of shift spaces

Manfred Denker, Atsushi Imai, Susanne Koch (2007)

Colloquium Mathematicae

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We define thin equivalence relations ∼ on shift spaces $^{\infty}$ and derive Dirichlet forms on the quotient space $Σ =^{\infty} / \sim$ in terms of the nearest neighbour averaging operator. We identify the associated Laplace operator. The conditions are applied to some non-self-similar extensions of the Sierpiński gasket.

Unit-regularity and representability for semiartinian $*$ -regular rings

Christian Herrmann (2020)

Archivum Mathematicum

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We show that any semiartinian $*$ -regular ring $R$ is unit-regular; if, in addition, $R$ is subdirectly irreducible then it admits a representation within some inner product space.

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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On an entire function represented by multiple Dirichlet series

Lakshika Chutani (2021)

Mathematica Bohemica

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Consider the space $L$ of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space $L$ the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained.

Remarks on absolutely regular and regular $K^{'} M_{p}$ -distributions

S. Pilipović (1991)

Annales Polonici Mathematici

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nbspAbstract. We give the definition of $K^{'} M_{P}$ regular distributions and some characterizations of absolutely regular and regular $K^{'} M_{p}$ -distributions.

Isometric composition operators on weighted Dirichlet space

Shi-An Han, Ze-Hua Zhou (2016)

Czechoslovak Mathematical Journal

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We investigate isometric composition operators on the weighted Dirichlet space $𝒟_{α}$ with standard weights ${(1 - | z |}^{2})^{α}$ , $α > - 1$ . The main technique used comes from Martín and Vukotić who completely characterized the isometric composition operators on the classical Dirichlet space $𝒟$ . We solve some of these but not in general. We also investigate the situation when $𝒟_{α}$ is equipped with another equivalent norm.

Universal completely regular dendrites

K. Omiljanowski, S. Zafiridou (2005)

Colloquium Mathematicae

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We define a dendrite $E_{n}$ which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite $E_{ω}$ is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite $D_{n}$ of order n described by J. J. Charatonik.

Envelope of Dirichlet problems on a domain in $C^{n}$

Eric Bedford (1985)

Annales Polonici Mathematici

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Potentials with respect to the pluricomplex Green function

Urban Cegrell (2012)

Annales Polonici Mathematici

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For μ a positive measure, we estimate the pluricomplex potential of μ, $P_{μ} (x) = \int_{Ω} g (x, y) d μ (y)$ , where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.

On discrete mean values of Dirichlet $L$ -functions

Ertan Elma (2021)

Czechoslovak Mathematical Journal

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Let $χ$ be a nonprincipal Dirichlet character modulo a prime number $p ⩾ 3$ and let $𝔞_{χ} : = \frac{1}{2} (1 - χ (- 1))$ . Define the mean value $ℳ_{p} (- s, χ) : = \frac{2}{p - 1} \sum ψ (mod p) ψ (- 1) = - 1 L (1, ψ) L (- s, χ \bar{ψ}) (σ : = ℜ s > 0) .$ We give an identity for $ℳ_{p} (- s, χ)$ which, in particular, shows that $ℳ_{p} (- s, χ) = L (1 - s, χ) + 𝔞_{χ} 2 p^{s} L (1, χ) ζ (- s) + o (1) (p \to \infty)$ for fixed $0 < σ < \frac{1}{2}$ and $| t : = ℑ s | = o (p^{(1 - 2 σ) / (3 + 2 σ)})$ .

Existence theorem for $n$ capacities

Marcel Brelot (1954)

Annales de l'institut Fourier

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On sait que la capacité d’un système de $n$ compacts est majorée par la somme des capacités ; on montre ici qu’on peut trouver $n$ compacts de capacités imposées $γ_{i}$ , tels que la réunion ait une capacité majorant $Σ_{γ_{i}} - ϵ$ ( $ϵ > 0$ donné à l’avance). Ce résultat établi ici dans un espace de Green avec le potentiel de Green était demandé par Choquet qui l’utilise dans sa théorie des capacités.