Displaying similar documents to “Universal Taylor series, conformal mappings and boundary behaviour”

Mobius invariant Besov spaces on the unit ball of n

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give new characterizations of the analytic Besov spaces B p on the unit ball 𝔹 of n in terms of oscillations and integral means over some Euclidian balls contained in 𝔹 .

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.

On a theorem of Lindelof

Vladimir Ya. Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give a quasiconformal version of the proof for the classical Lindelof theorem: Let f map the unit disk 𝔻 conformally onto the inner domain of a Jordan curve 𝒞 : Then 𝒞 is smooth if and only if arg f ' ( z ) has a continuous extension to 𝔻 ¯ . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.

On the continuity of Hausdorff dimension of Julia sets and similarity between the Mandelbrot set and Julia sets

Juan Rivera-Letelier (2001)

Fundamenta Mathematicae

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Given d ≥ 2 consider the family of polynomials P c ( z ) = z d + c for c ∈ ℂ. Denote by J c the Julia set of P c and let d = c | J c i s c o n n e c t e d be the connectedness locus; for d = 2 it is called the Mandelbrot set. We study semihyperbolic parameters c d : those for which the critical point 0 is not recurrent by P c and without parabolic cycles. The Hausdorff dimension of J c , denoted by H D ( J c ) , does not depend continuously on c at such c d ; on the other hand the function c H D ( J c ) is analytic in - d . Our first result asserts that there is still some...

A symmetry problem in the calculus of variations

Graziano Crasta (2006)

Journal of the European Mathematical Society

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We consider the integral functional J ( u ) = Ω [ f ( | D u | ) u ] d x , u W 0 1 , 1 ( Ω ) , where Ω n , n 2 , is a nonempty bounded connected open subset of n with smooth boundary, and s f ( | s | ) is a convex, differentiable function. We prove that if J admits a minimizer in W 0 1 , 1 ( Ω ) depending only on the distance from the boundary of Ω , then Ω must be a ball.

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...

The almost Einstein operator for ( 2 , 3 , 5 ) distributions

Katja Sagerschnig, Travis Willse (2017)

Archivum Mathematicum

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For the geometry of oriented ( 2 , 3 , 5 ) distributions ( M , ) , which correspond to regular, normal parabolic geometries of type ( G 2 , P ) for a particular parabolic subgroup P < G 2 , we develop the corresponding tractor calculus and use it to analyze the first BGG operator Θ 0 associated to the 7 -dimensional irreducible representation of G 2 . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions...

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...

1 -cocycles on the group of contactomorphisms on the supercircle S 1 | 3 generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

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The relative cohomology H diff 1 ( 𝕂 ( 1 | 3 ) , 𝔬𝔰𝔭 ( 2 , 3 ) ; 𝒟 λ , μ ( S 1 | 3 ) ) of the contact Lie superalgebra 𝕂 ( 1 | 3 ) with coefficients in the space of differential operators 𝒟 λ , μ ( S 1 | 3 ) acting on tensor densities on S 1 | 3 , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1 -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1 -cocycle s ( X f ) = D 1 D 2 D 3 ( f ) α 3 1 / 2 , X f 𝕂 ( 1 | 3 ) which is invariant with respect to the conformal subsuperalgebra 𝔬𝔰𝔭 ( 2 , 3 ) of 𝕂 ( 1 | 3 ) . In this work we study the supergroup case. We give an explicit construction of 1 -cocycles...

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...

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...

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 .

On compactness and connectedness of the paratingent

Wojciech Zygmunt (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this note we shall prove that for a continuous function ϕ : Δ n , where Δ ,  the paratingent of ϕ at a Δ is a non-empty and compact set in n if and only if ϕ satisfies Lipschitz condition in a neighbourhood of a . Moreover, in this case the paratingent is a connected set.

On a result by Clunie and Sheil-Small

Dariusz Partyka, Ken-ichi Sakan (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk 𝔻 , if F ( 𝔻 ) is a convex domain, then the inequality | G ( z 2 ) - G ( z 1 ) | < | H ( z 2 ) - H ( z 1 ) | holds for all distinct points z 1 , z 2 𝔻 . Here H and G are holomorphic mappings in 𝔻 determined by F = H + G ¯ , up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain Ω in and improve it provided F is additionally a quasiconformal mapping...

On sums and products in a field

Guang-Liang Zhou, Zhi-Wei Sun (2022)

Czechoslovak Mathematical Journal

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We study sums and products in a field. Let F be a field with ch ( F ) 2 , where ch ( F ) is the characteristic of F . For any integer k 4 , we show that any x F can be written as a 1 + + a k with a 1 , , a k F and a 1 a k = 1 , and that for any α F { 0 } we can write every x F as a 1 a k with a 1 , , a k F and a 1 + + a k = α . We also prove that for any x F and k { 2 , 3 , } there are a 1 , , a 2 k F such that a 1 + + a 2 k = x = a 1 a 2 k .