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Displaying similar documents to “The ideal boundary of a domain in C n

Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang (2014)

Annales Polonici Mathematici

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Let A ζ = Ω - ρ ( ζ ) · Ω ¯ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel K ζ ( z ) of A ζ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that A ζ is non-pseudoconvex when the dimension of A ζ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for ² l o g K ζ / ζ ζ ̅ , as well as its boundary behavior.

Espace de Dixmier des opérateurs de Hankel sur les espaces de Bergman à poids

Romaric Tytgat (2015)

Czechoslovak Mathematical Journal

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Nous donnons des résultats théoriques sur l’idéal de Macaev et la trace de Dixmier. Ensuite, nous caractérisons les symboles antiholomorphes f ¯ tels que l’opérateur de Hankel H f ¯ sur l’espace de Bergman à poids soit dans l’idéal de Macaev et nous donnons la trace de Dixmier. Pour cela, nous regardons le comportement des normes de Schatten 𝒮 p quand p tend vers 1 et nous nous appuyons sur le résultat de Engliš et Rochberg sur l’espace de Bergman. Nous parlons aussi des puissances de tels opérateurs....

Bounded evaluation operators from H p into q

Martin Smith (2007)

Studia Mathematica

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Given 0 < p,q < ∞ and any sequence z = zₙ in the unit disc , we define an operator from functions on to sequences by T z , p ( f ) = ( 1 - | z | ² ) 1 / p f ( z ) . Necessary and sufficient conditions on zₙ are given such that T z , p maps the Hardy space H p boundedly into the sequence space q . A corresponding result for Bergman spaces is also stated.

Duality of measures of non-𝒜-compactness

Juan Manuel Delgado, Cándido Piñeiro (2015)

Studia Mathematica

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Let be a Banach operator ideal. Based on the notion of -compactness in a Banach space due to Carl and Stephani, we deal with the notion of measure of non–compactness of an operator. We consider a map χ (respectively, n ) acting on the operators of the surjective (respectively, injective) hull of such that χ ( T ) = 0 (respectively, n ( T ) = 0 ) if and only if the operator T is -compact (respectively, injectively -compact). Under certain conditions on the ideal , we prove an equivalence inequality involving...

Ideals in big Lipschitz algebras of analytic functions

Thomas Vils Pedersen (2004)

Studia Mathematica

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For 0 < γ ≤ 1, let Λ γ be the big Lipschitz algebra of functions analytic on the open unit disc which satisfy a Lipschitz condition of order γ on ̅. For a closed set E on the unit circle and an inner function Q, let J γ ( E , Q ) be the closed ideal in Λ γ consisting of those functions f Λ γ for which (i) f = 0 on E, (ii) | f ( z ) - f ( w ) | = o ( | z - w | γ ) as d(z,E),d(w,E) → 0, (iii) f / Q Λ γ . Also, for a closed ideal I in Λ γ , let E I = z ∈ : f(z) = 0 for every f ∈ I and let Q I be the greatest common divisor of the inner parts of non-zero functions...

Semi n -ideals of commutative rings

Ece Yetkin Çelikel, Hani A. Khashan (2022)

Czechoslovak Mathematical Journal

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Let R be a commutative ring with identity. A proper ideal I is said to be an n -ideal of R if for a , b R , a b I and a 0 imply b I . We give a new generalization of the concept of n -ideals by defining a proper ideal I of R to be a semi n -ideal if whenever a R is such that a 2 I , then a 0 or a I . We give some examples of semi n -ideal and investigate semi n -ideals under various contexts of constructions such as direct products, homomorphic images and localizations. We present various characterizations of this new...

A note on the multiplier ideals of monomial ideals

Cheng Gong, Zhongming Tang (2015)

Czechoslovak Mathematical Journal

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Let 𝔞 [ x 1 , ... , x n ] be a monomial ideal and 𝒥 ( 𝔞 c ) the multiplier ideal of 𝔞 with coefficient c . Then 𝒥 ( 𝔞 c ) is also a monomial ideal of [ x 1 , ... , x n ] , and the equality 𝒥 ( 𝔞 c ) = 𝔞 implies that 0 < c < n + 1 . We mainly discuss the problem when 𝒥 ( 𝔞 ) = 𝔞 or 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 for all 0 < ε < 1 . It is proved that if 𝒥 ( 𝔞 ) = 𝔞 then 𝔞 is principal, and if 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 holds for all 0 < ε < 1 then 𝔞 = ( x 1 , ... , x n ) . One global result is also obtained. Let 𝔞 ˜ be the ideal sheaf on n - 1 associated with 𝔞 . Then it is proved that the equality 𝒥 ( 𝔞 ˜ ) = 𝔞 ˜ implies that 𝔞 ˜ is principal.

Extension of germs of holomorphic isometries up to normalizing constants with respect to the Bergman metric

Ngaiming Mok (2012)

Journal of the European Mathematical Society

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We study the extension problem for germs of holomorphic isometries f : ( D ; x 0 ) ( Ω ; f ( x 0 ) ) up to normalizing constants between bounded domains in Euclidean spaces equipped with Bergman metrics d s D 2 on D and d s Ω 2 on Ω . Our main focus is on boundary extension for pairs of bounded domains ( D , Ω ) such that the Bergman kernel K D ( z , w ) extends meromorphically in ( z , w ¯ ) to a neighborhood of D ¯ × D , and such that the analogous statement holds true for the Bergman kernel K Ω ( ς , ξ ) on Ω . Assuming that ( D ; d s D 2 ) and ( Ω ; d s Ω 2 ) are complete Kähler manifolds, we prove that...

The strong persistence property and symbolic strong persistence property

Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)

Czechoslovak Mathematical Journal

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Let I be an ideal in a commutative Noetherian ring R . Then the ideal I has the strong persistence property if and only if ( I k + 1 : R I ) = I k for all k , and I has the symbolic strong persistence property if and only if ( I ( k + 1 ) : R I ( 1 ) ) = I ( k ) for all k , where I ( k ) denotes the k th symbolic power of I . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial...

Some generalizations of Olivier's theorem

Alain Faisant, Georges Grekos, Ladislav Mišík (2016)

Mathematica Bohemica

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Let n = 1 a n be a convergent series of positive real numbers. L. Olivier proved that if the sequence ( a n ) is non-increasing, then lim n n a n = 0 . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n n a n = 0 ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence...

Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups

Lingli Zeng, Jizhu Nan (2016)

Czechoslovak Mathematical Journal

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Let F be a finite field of characteristic p and K a field which contains a primitive p th root of unity and char K p . Suppose that a classical group G acts on the F -vector space V . Then it can induce the actions on the vector space V V and on the group algebra K [ V V ] , respectively. In this paper we determine the structure of G -invariant ideals of the group algebra K [ V V ] , and establish the relationship between the invariant ideals of K [ V ] and the vector invariant ideals of K [ V V ] , if G is a unitary group or orthogonal...

Continuous pluriharmonic boundary values

Per Åhag, Rafał Czyż (2007)

Annales Polonici Mathematici

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Let D j be a bounded hyperconvex domain in n j and set D = D × × D s , j=1,...,s, s≥ 3. Also let ₙ be the symmetrized polydisc in ℂⁿ, n ≥ 3. We characterize those real-valued continuous functions defined on the boundary of D or ₙ which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.