On the algebra of $A^k$-functions

Ulf Backlund; Anders Fällström

Displaying similar documents to “On the algebra of $A^k$-functions”

Weak lineal convexity

Christer O. Kiselman (2015)

Banach Center Publications

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A bounded open set with boundary of class C¹ which is locally weakly lineally convex is weakly lineally convex, but, as shown by Yuriĭ Zelinskiĭ, this is not true for unbounded domains. The purpose here is to construct explicit examples, Hartogs domains, showing this. Their boundary can have regularity $C^{1, 1}$ or $C^{\infty}$ . Obstructions to constructing smoothly bounded domains with certain homogeneity properties will be discussed.

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

J. Siciak (1985)

Matematički Vesnik

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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 $ℋ^{\infty} (G)$ .

Canonical mappings in $Σ_{M} (D)$

Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)

Matematički Vesnik

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Global boundary regularity for the $\bar{p a r t i a l}$ -equation on $q$ -pseudo-convex domains

Heungju Ahn (2005)

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

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For a bounded domain $D$ of $C^{n}$ , we introduce a notion of « $q$ -pseudoconvexity» of new type and prove that for a given $\bar{\partial}$ -closed $(p, r)$ -form $f$ that is smooth up to the boundary on $D$ , and for $r \geq q$ , there exists a $(p, r - 1)$ -form $u$ smooth up to the boundary on $D$ which is a solution of the equation $\bar{\partial} u = f$

Certain partial differential subordinations on some Reinhardt domains in $ℂ^{n}$

Gabriela Kohr, Mirela Kohr (1997)

Annales Polonici Mathematici

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We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in $ℂ^{n}$ . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain $B_{2 p}$ with p ≥ 1.

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 $ℂ^{N}$ .

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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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 $\mathbf{C}^{k}$ .

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in $C^{n}$ with real analytic boundary

Andrea Iannuzzi (1994)

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

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It is shown that given a bounded strictly convex domain $Ω$ in $C^{n}$ with real analitic boundary and a point $x_{0}$ in $Ω$ , there exists a larger bounded strictly convex domain $Ω^{'}$ with real analitic boundary, close as wished to $Ω$ , such that $Ω$ is a ball for the Kobayashi distance of $Ω^{'}$ with center $x_{0}$ . The result is applied to prove that if $Ω$ is not biholomorphic to the ball then any automorphism of $Ω$ extends to an automorphism of $Ω^{'}$ .

Diametral dimension of some pseudoconvex multiscale spaces

Jean-Marie Aubry, Françoise Bastin (2010)

Studia Mathematica

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Stemming from the study of signals via wavelet coefficients, the spaces $S^{ν}$ are complete metrizable and separable topological vector spaces, parametrized by a function ν, whose elements are sequences indexed by a binary tree. Several papers were devoted to their basic topology; recently it was also shown that depending on ν, $S^{ν}$ may be locally convex, locally p-convex for some p > 0, or not at all, but under a minor condition these spaces are always pseudoconvex. We deal with some more...

$L ²_{h}$ -domains of holomorphy and the Bergman kernel

Peter Pflug, Włodzimierz Zwonek (2002)

Studia Mathematica

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We give a characterization of $L ²_{h}$ -domains of holomorphy with the help of the boundary behavior of the Bergman kernel and geometric properties of the boundary, respectively.