Width asymptotics for a pair of Reinhardt domains

A. Aytuna; A. Rashkovskii; V. Zahariuta

Displaying similar documents to “Width asymptotics for a pair of Reinhardt domains”

On n-circled $ℋ^{\infty}$ -domains of holomorphy

Marek Jarnicki, Peter Pflug (1997)

Annales Polonici Mathematici

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We present various characterizations of n-circled domains of holomorphy $G \subset ℂ^{n}$ with respect to some subspaces of $ℋ^{\infty} (G)$ .

On the paradox of two $R_{1}, R_{2}$ domains in Schwarzschild exterior solution

A. Zięba (1972)

Colloquium Mathematicae

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A domain whose envelope of holomorphy is not a domain

Edgar Lee Stout (2006)

Annales Polonici Mathematici

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We construct a domain of holomorphy in $ℂ^{N}$ , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in $ℂ^{N}$ .

Pluriharmonic extension in proper image domains

Rafał Czyż (2009)

Annales Polonici Mathematici

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Let $D_{j}$ be a bounded hyperconvex domain in $ℂ^{n_{j}}$ and set $D = D ₁ \times \dots \times D_{s}$ , j=1,...,s, s ≥ 3. Also let $Ω_{π}$ be the image of D under the proper holomorphic map π. We characterize those continuous functions $f : \partial Ω_{π} \to ℝ$ that can be extended to a real-valued pluriharmonic function in $Ω_{π}$ .

$H^{p}$ spaces on bounded symmetric domains

Kyong T. Hahn, Josephine Mitchell (1973)

Annales Polonici Mathematici

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Multiple end solutions to the Allen-Cahn equation in $ℝ^{2}$

Michał Kowalczyk, Yong Liu, Frank Pacard (2013-2014)

Séminaire Laurent Schwartz — EDP et applications

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An entire solution of the Allen-Cahn equation $Δ u = f (u)$ , where $f$ is an odd function and has exactly three zeros at $\pm 1$ and $0$ , e.g. $f (u) = u (u^{2} - 1)$ , is called a $2 k$ end solution if its nodal set is asymptotic to $2 k$ half lines, and if along each of these half lines the function $u$ looks (up to a multiplication by $- 1$ ) like the one dimensional, odd, heteroclinic solution $H$ , of $H^{''} = f (H)$ . In this paper we present some recent advances in the theory of the multiple end solutions. We begin with the description of the moduli space...

A remark on separate holomorphy

Marek Jarnicki, Peter Pflug (2006)

Studia Mathematica

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Let X be a Riemann domain over $ℂ^{k} \times ℂ^{ℓ}$ . If X is a domain of holomorphy with respect to a family ℱ ⊂(X), then there exists a pluripolar set $P \subset ℂ^{k}$ such that every slice $X_{a}$ of X with a∉ P is a region of holomorphy with respect to the family ${f |}_{X_{a}} : f \in ℱ$ .

The equation $\bar{\partial}u=f$ the intersection of pseudoconvex domains

Alessandro Perotti (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Viene studiata l'equazione $\bar{\partial}u=f$ per le forme regolari sulla chiusura dell'intersezione di $k$ domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme $\mathbf{C}^{k}$ .

When $C_{p} (X)$ is domain representable

William Fleissner, Lynne Yengulalp (2013)

Fundamenta Mathematicae

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Let M be a metrizable group. Let G be a dense subgroup of $M^{X}$ . We prove that if G is domain representable, then $G = M^{X}$ . The following corollaries answer open questions. If X is completely regular and $C_{p} (X)$ is domain representable, then X is discrete. If X is zero-dimensional, T₂, and $C_{p} (X,)$ is subcompact, then X is discrete.

The $L^{2}$ $\bar{\partial}$ -Cauchy problem on weakly $q$ -pseudoconvex domains in Stein manifolds

Sayed Saber (2015)

Czechoslovak Mathematical Journal

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Let $X$ be a Stein manifold of complex dimension $n \geq 2$ and $Ω ⋐ X$ be a relatively compact domain with $C^{2}$ smooth boundary in $X$ . Assume that $Ω$ is a weakly $q$ -pseudoconvex domain in $X$ . The purpose of this paper is to establish sufficient conditions for the closed range of $\bar{\partial}$ on $Ω$ . Moreover, we study the $\bar{\partial}$ -problem on $Ω$ . Specifically, we use the modified weight function method to study the weighted $\bar{\partial}$ -problem with exact support in $Ω$ . Our method relies on the $L^{2}$ -estimates by Hörmander (1965) and by Kohn (1973). ...

On coarse embeddability into $ℓ_{p}$ -spaces and a conjecture of Dranishnikov

Piotr W. Nowak (2006)

Fundamenta Mathematicae

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We show that the Hilbert space is coarsely embeddable into any $ℓ_{p}$ for 1 ≤ p ≤ ∞. It follows that coarse embeddability into ℓ₂ and into $ℓ_{p}$ are equivalent for 1 ≤ p < 2.

Curved thin domains and parabolic equations

M. Prizzi, M. Rinaldi, K. P. Rybakowski (2002)

Studia Mathematica

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Consider the family uₜ = Δu + G(u), t > 0, $x \in Ω_{ε}$ , $\partial_{ν_{ε}} u = 0$ , t > 0, $x \in \partial Ω_{ε}$ , $(E_{ε})$ of semilinear Neumann boundary value problems, where, for ε > 0 small, the set $Ω_{ε}$ is a thin domain in $ℝ^{l}$ , possibly with holes, which collapses, as ε → 0⁺, onto a (curved) k-dimensional submanifold of $ℝ^{l}$ . If G is dissipative, then equation $(E_{ε})$ has a global attractor $_{ε}$ . We identify a “limit” equation for the family $(E_{ε})$ , prove convergence of trajectories and establish an upper semicontinuity result for the family $_{ε}$ as ε → 0⁺. ...

The method of rotation and Marcinkiewicz integrals on product domains

Jiecheng Chen, Dashan Fan, Yiming Ying (2002)

Studia Mathematica

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We give some rather weak sufficient condition for $L^{p}$ boundedness of the Marcinkiewicz integral operator $μ_{Ω}$ on the product spaces $ℝ ⁿ \times ℝ^{m}$ (1 < p < ∞), which improves and extends some known results.

On the UMD constant of the space $ℓ ₁^{N}$

Adam Osękowski (2016)

Colloquium Mathematicae

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Let N ≥ 2 be a given integer. Suppose that $d f = {(d f ₙ)}_{n \geq 0}$ is a martingale difference sequence with values in $ℓ ₁^{N}$ and let ${(ε ₙ)}_{n \geq 0}$ be a deterministic sequence of signs. The paper contains the proof of the estimate $ℙ (s u p_{n \geq 0} | | \sum_{k = 0}^{n} ε_{k} d f_{k} {| |}_{ℓ ₁^{N}} \geq 1) \leq (l n N + l n (3 l n N)) / (1 - {(2 l n N)}^{- 1}) s u p_{n \geq 0} | | \sum_{k = 0}^{n} d f_{k} {| |}_{ℓ ₁^{N}}$ . It is shown that this result is asymptotically sharp in the sense that the least constant $C_{N}$ in the above estimate satisfies $l i m_{N \to \infty} C_{N} / l n N = 1$ . The novelty in the proof is the explicit verification of the ζ-convexity of the space $ℓ ₁^{N}$ .

Balanced domains of holomorphy of type $H^{α}$

J. Siciak (1985)

Matematički Vesnik

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The equation $\bar{\partial}u=f$ the intersection of pseudoconvex domains

Alessandro Perotti (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Characterization of cycle domains via Kobayashi hyperbolicity

Gregor Fels, Alan Huckleberry (2005)

Bulletin de la Société Mathématique de France

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A real form $G$ of a complex semi-simple Lie group $G^{ℂ}$ has only finitely many orbits in any given $G^{ℂ}$ -flag manifold $Z = G^{ℂ} / Q$ . The complex geometry of these orbits is of interest, e.g., for the associated representation theory. The open orbits $D$ generally possess only the constant holomorphic functions, and the relevant associated geometric objects are certain positive-dimensional compact complex submanifolds of $D$ which, with very few well-understood exceptions, are parameterized by the Wolf cycle...

Fields of moduli of three-point $G$ -covers with cyclic $p$ -Sylow, II

Andrew Obus (2013)

Journal de Théorie des Nombres de Bordeaux

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We continue the examination of the stable reduction and fields of moduli of $G$ -Galois covers of the projective line over a complete discrete valuation field of mixed characteristic $(0, p)$ , where $G$ has a $p$ -Sylow subgroup $P$ of order $p^{n}$ . Suppose further that the normalizer of $P$ acts on $P$ via an involution. Under mild assumptions, if $f : Y \to ℙ^{1}$ is a three-point $G$ -Galois cover defined over $\bar{ℚ}$ , then the $n$ th higher ramification groups above $p$ for the upper numbering of the (Galois closure of...

A pure smoothness condition for Radó’s theorem for $α$ -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

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Let $Ω \subset ℂ^{n}$ be a bounded, simply connected $ℂ$ -convex domain. Let $α \in ℤ_{+}^{n}$ and let $f$ be a function on $Ω$ which is separately $C^{2 α_{j} - 1}$ -smooth with respect to $z_{j}$ (by which we mean jointly $C^{2 α_{j} - 1}$ -smooth with respect to $Re z_{j}$ , $Im z_{j}$ ). If $f$ is $α$ -analytic on $Ω ∖ f^{- 1} (0)$ , then $f$ is $α$ -analytic on $Ω$ . The result is well-known for the case $α_{i} = 1$ , $1 \leq i \leq n$ , even when $f$ a priori is only known to be continuous.

Existence and regularity of solutions of some elliptic system in domains with edges

Wojciech M. Zajączkowski

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CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in $D_{ϑ}$ ...............................................346. Existence of solutions of (3.14) in $H_{μ}^{k} (D_{ϑ})$ ............417. Green function................................................................528....

Moduli of smoothness of functions and their derivatives

Z. Ditzian, S. Tikhonov (2007)

Studia Mathematica

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Relations between moduli of smoothness of the derivatives of a function and those of the function itself are investigated. The results are for $L_{p} (T)$ and $L_{p} [- 1, 1]$ for 0 < p < ∞ using the moduli of smoothness $ω^{r} {(f, t)}_{p}$ and $ω_{φ}^{r} {(f, t)}_{p}$ respectively.

On a conjecture of Dekking : The sum of digits of even numbers

Iurie Boreico, Daniel El-Baz, Thomas Stoll (2014)

Journal de Théorie des Nombres de Bordeaux

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Let $q \geq 2$ and denote by $s_{q}$ the sum-of-digits function in base $q$ . For $j = 0, 1, \dots, q - 1$ consider $# {0 \leq n < N : s_{q} (2 n) \equiv j (mod q)} .$ In 1983, F. M. Dekking conjectured that this quantity is greater than $N / q$ and, respectively, less than $N / q$ for infinitely many $N$ , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.