Displaying similar documents to “Shilov boundary for holomorphic functions on some classical Banach spaces”

Spaces of geometrically generic configurations

Yoel Feler (2008)

Journal of the European Mathematical Society

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Let X denote either ℂℙ m or m . We study certain analytic properties of the space n ( X , g p ) of ordered geometrically generic n -point configurations in X . This space consists of all q = ( q 1 , , q n ) X n such that no m + 1 of the points q 1 , , q n belong to a hyperplane in X . In particular, we show that for a big enough n any holomorphic map f : n ( ℂℙ m , g p ) n ( ℂℙ m , g p ) commuting with the natural action of the symmetric group 𝐒 ( n ) in n ( ℂℙ m , g p ) is of the form f ( q ) = τ ( q ) q = ( τ ( q ) q 1 , , τ ( q ) q n ) , q n ( ℂℙ m , g p ) , where τ : n ( ℂℙ m , g p ) 𝐏𝐒𝐋 ( m + 1 , ) is an 𝐒 ( n ) -invariant holomorphic map. A similar result holds true for mappings of the configuration...

J -holomorphic discs and real analytic hypersurfaces

William Alexandre, Emmanuel Mazzilli (2014)

Annales de l’institut Fourier

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We give in 6 a real analytic almost complex structure J , a real analytic hypersurface M and a vector v in the Levi null set at 0 of M , such that there is no germ of J -holomorphic disc γ included in M with γ ( 0 ) = 0 and γ x ( 0 ) = v , although the Levi form of M has constant rank. Then for any hypersurface M and any complex structure J , we give sufficient conditions under which there exists such a germ of disc.

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 n j and set D = D × × 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 : Ω π that can be extended to a real-valued pluriharmonic function in Ω π .

New characterizations for weighted composition operator from Zygmund type spaces to Bloch type spaces

Xin-Cui Guo, Ze-Hua Zhou (2015)

Czechoslovak Mathematical Journal

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Let u be a holomorphic function and ϕ a holomorphic self-map of the open unit disk 𝔻 in the complex plane. We provide new characterizations for the boundedness of the weighted composition operators u C ϕ from Zygmund type spaces to Bloch type spaces in 𝔻 in terms of u , ϕ , their derivatives, and ϕ n , the n -th power of ϕ . Moreover, we obtain some similar estimates for the essential norms of the operators u C ϕ , from which sufficient and necessary conditions of compactness of u C ϕ follows immediately. ...

Steinness of bundles with fiber a Reinhardt bounded domain

Karl Oeljeklaus, Dan Zaffran (2006)

Bulletin de la Société Mathématique de France

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Let E denote a holomorphic bundle with fiber D and with basis B . Both D and B are assumed to be Stein. For D a Reinhardt bounded domain of dimension d = 2 or 3 , we give a necessary and sufficient condition on D for the existence of a non-Stein such E (Theorem 1 ); for d = 2 , we give necessary and sufficient criteria for E to be Stein (Theorem 2 ). For D a Reinhardt bounded domain of any dimension not intersecting any coordinate hyperplane, we give a sufficient criterion for E to be Stein (Theorem...

Equidistribution towards the Green current for holomorphic maps

Tien-Cuong Dinh, Nessim Sibony (2008)

Annales scientifiques de l'École Normale Supérieure

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Let f be a non-invertible holomorphic endomorphism of a projective space and f n its iterate of order n . We prove that the pull-back by f n of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to f when n tends to infinity. We also give an analogous result for the pull-back of positive closed ( 1 , 1 ) -currents and a similar result for regular polynomial automorphisms of  k .

The weak Gelfand-Phillips property in spaces of compact operators

Ioana Ghenciu (2017)

Commentationes Mathematicae Universitatis Carolinae

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For Banach spaces X and Y , let K w * ( X * , Y ) denote the space of all w * - w continuous compact operators from X * to Y endowed with the operator norm. A Banach space X has the w G P property if every Grothendieck subset of X is relatively weakly compact. In this paper we study Banach spaces with property w G P . We investigate whether the spaces K w * ( X * , Y ) and X ϵ Y have the w G P property, when X and Y have the w G P property.

Holomorphic line bundles and divisors on a domain of a Stein manifold

Makoto Abe (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let D be an open set of a Stein manifold X of dimension n such that H k ( D , 𝒪 ) = 0 for 2 k n - 1 . We prove that D is Stein if and only if every topologically trivial holomorphic line bundle L on D is associated to some Cartier divisor 𝔡 on D .

Some theorems of Korovkin type

Tomoko Hachiro, Takateru Okayasu (2003)

Studia Mathematica

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We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, C ( X ) ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., C ( Y ) ), and ϕ a linear isometry from M into C(Y) (resp., C ( Y ) ). We show, under the assumption that Π N Π T , where Π N is...

Non-isotropic Hausdorff capacity of exceptional sets for pluri-Green potentials in the unit ball of ℂⁿ

Kuzman Adzievski (2006)

Annales Polonici Mathematici

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We study questions related to exceptional sets of pluri-Green potentials V μ in the unit ball B of ℂⁿ in terms of non-isotropic Hausdorff capacity. For suitable measures μ on the ball B, the pluri-Green potentials V μ are defined by V μ ( z ) = B l o g ( 1 / | ϕ z ( w ) | ) d μ ( w ) , where for a fixed z ∈ B, ϕ z denotes the holomorphic automorphism of B satisfying ϕ z ( 0 ) = z , ϕ z ( z ) = 0 and ( ϕ z ϕ z ) ( w ) = w for every w ∈ B. If dμ(w) = f(w)dλ(w), where f is a non-negative measurable function of B, and λ is the measure on B, invariant under all holomorphic automorphisms of...

Equidistribution towards the Green current

Vincent Guedj (2003)

Bulletin de la Société Mathématique de France

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Let f : k k be a dominating rational mapping of first algebraic degree λ 2 . If S is a positive closed current of bidegree ( 1 , 1 ) on k with zero Lelong numbers, we show – under a natural dynamical assumption – that the pullbacks λ - n ( f n ) * S converge to the Green current T f . For some families of mappings, we get finer convergence results which allow us to characterize all f * -invariant currents.

Existence of positive solutions for second order m-point boundary value problems

Ruyun Ma (2002)

Annales Polonici Mathematici

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Let α,β,γ,δ ≥ 0 and ϱ:= γβ + αγ + αδ > 0. Let ψ(t) = β + αt, ϕ(t) = γ + δ - γt, t ∈ [0,1]. We study the existence of positive solutions for the m-point boundary value problem ⎧u” + h(t)f(u) = 0, 0 < t < 1, ⎨ α u ( 0 ) - β u ' ( 0 ) = i = 1 m - 2 a i u ( ξ i ) γ u ( 1 ) + δ u ' ( 1 ) = i = 1 m - 2 b i u ( ξ i ) , where ξ i ( 0 , 1 ) , a i , b i ( 0 , ) (for i ∈ 1,…,m-2) are given constants satisfying ϱ - i = 1 m - 2 a i ϕ ( ξ i ) > 0 , ϱ - i = 1 m - 2 b i ψ ( ξ i ) > 0 and Δ : = - i = 1 m - 2 a i ψ ( ξ i ) ϱ - i = 1 m - 2 a i ϕ ( ξ i ) ϱ - i = 1 m - 2 b i ψ ( ξ i ) - i = 1 m - 2 b i ϕ ( ξ i ) < 0 . We show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and...

Recurrence and mixing recurrence of multiplication operators

Mohamed Amouch, Hamza Lakrimi (2024)

Mathematica Bohemica

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Let X be a Banach space, ( X ) the algebra of bounded linear operators on X and ( J , · J ) an admissible Banach ideal of ( X ) . For T ( X ) , let L J , T and R J , T ( J ) denote the left and right multiplication defined by L J , T ( A ) = T A and R J , T ( A ) = A T , respectively. In this paper, we study the transmission of some concepts related to recurrent operators between T ( X ) , and their elementary operators L J , T and R J , T . In particular, we give necessary and sufficient conditions for L J , T and R J , T to be sequentially recurrent. Furthermore, we prove that L J , T is recurrent...

3x+1 inverse orbit generating functions almost always have natural boundaries

Jason P. Bell, Jeffrey C. Lagarias (2015)

Acta Arithmetica

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The 3x+k function T k ( n ) sends n to (3n+k)/2, resp. n/2, according as n is odd, resp. even, where k ≡ ±1 (mod 6). The map T k ( · ) sends integers to integers; for m ≥1 let n → m mean that m is in the forward orbit of n under iteration of T k ( · ) . We consider the generating functions f k , m ( z ) = n > 0 , n m z n , which are holomorphic in the unit disk. We give sufficient conditions on (k,m) for the functions f k , m ( z ) to have the unit circle |z|=1 as a natural boundary to analytic continuation. For the 3x+1 function these conditions hold...

𝒞 k -regularity for the ¯ -equation with a support condition

Shaban Khidr, Osama Abdelkader (2017)

Czechoslovak Mathematical Journal

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Let D be a 𝒞 d q -convex intersection, d 2 , 0 q n - 1 , in a complex manifold X of complex dimension n , n 2 , and let E be a holomorphic vector bundle of rank N over X . In this paper, 𝒞 k -estimates, k = 2 , 3 , , , for solutions to the ¯ -equation with small loss of smoothness are obtained for E -valued ( 0 , s ) -forms on D when n - q s n . In addition, we solve the ¯ -equation with a support condition in 𝒞 k -spaces. More precisely, we prove that for a ¯ -closed form f in 𝒞 0 , q k ( X D , E ) , 1 q n - 2 , n 3 , with compact support and for ε with 0 < ε < 1 there...

Positivity and anti-maximum principles for elliptic operators with mixed boundary conditions

Catherine Bandle, Joachim von Below, Wolfgang Reichel (2008)

Journal of the European Mathematical Society

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We consider linear elliptic equations - Δ u + q ( x ) u = λ u + f in bounded Lipschitz domains D N with mixed boundary conditions u / n = σ ( x ) λ u + g on D . The main feature of this boundary value problem is the appearance of λ both in the equation and in the boundary condition. In general we make no assumption on the sign of the coefficient σ ( x ) . We study positivity principles and anti-maximum principles. One of our main results states that if σ is somewhere negative, q 0 and D q ( x ) d x > 0 then there exist two eigenvalues λ - 1 , λ 1 such the positivity...