The analytic -capacity and the Cauchy integral
K. Adžievski (1986)
Matematički Vesnik
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K. Adžievski (1986)
Matematički Vesnik
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Ryan M. Causey, Gilles Lancien (2023)
Commentationes Mathematicae Universitatis Carolinae
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For , we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent -asymptotically uniformly smooth norm. We prove that this class is analytic complete in the class of separable Banach spaces. These results extend previous works by N. J. Kalton, D. Werner and O. Kurka in the case .
D. Freeman, E. Odell, Th. Schlumprecht, A. Zsák (2009)
Fundamenta Mathematicae
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For every α < ω₁ we establish the existence of a separable Banach space whose Szlenk index is and which is universal for all separable Banach spaces whose Szlenk index does not exceed . In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with Tsirelson type upper estimates.
M. K. Aouf (1989)
Matematički Vesnik
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J. Siciak (1969)
Annales Polonici Mathematici
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B. Cascales, I. Namioka (2003)
Fundamenta Mathematicae
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In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is...
T. Gaspari (2002)
Studia Mathematica
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We study the set f’(X) = f’(x): x ∈ X when f:X → ℝ is a differentiable bump. We first prove that for any C²-smooth bump f: ℝ² → ℝ the range of the derivative of f must be the closure of its interior. Next we show that if X is an infinite-dimensional separable Banach space with a -smooth bump b:X → ℝ such that is finite, then any connected open subset of X* containing 0 is the range of the derivative of a -smooth bump. We also study the finite-dimensional case which is quite different....
V. Farmaki (1987)
Fundamenta Mathematicae
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Christian Le Merdy (2007)
Banach Center Publications
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To any bounded analytic semigroup on Hilbert space or on -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative -spaces, Banach lattices, and their subspaces. We give some applications to functional calculus, similarity problems, multiplier theory, and control theory.
Ting-Bin Cao, Zhong-Shu Deng (2010)
Annales Polonici Mathematici
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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation , where all coefficients , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.
Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv (2018)
Mathematica Bohemica
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We generalize some criteria of boundedness of -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).
E. Odell, Th. Schlumprecht, A. Zsák (2007)
Studia Mathematica
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For a countable ordinal α we denote by the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each admits a separable, reflexive universal space. We also show that spaces in the class embed into spaces of the same class with a basis. As a consequence we deduce that each is analytic in the Effros-Borel structure of subspaces of C[0,1].
Wilhelmina Smajdor (1970)
Annales Polonici Mathematici
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Wolfgang Tutschke (1983)
Banach Center Publications
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Jan Stochel, F. H. Szafraniec (1997)
Annales Polonici Mathematici
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The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.
Salvador Addas-Zanata, Pedro A. S. Salomão (2014)
Fundamenta Mathematicae
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Let f: S¹ × [0,1] → S¹ × [0,1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift f̃: ℝ × [0,1] → ℝ × [0,1] we have Fix(f̃) = ℝ × 0 and that f̃ positively translates points in ℝ × 1. Let be the perturbation of f̃ by the rigid horizontal translation (x,y) ↦ (x+ϵ,y). We show that for all ϵ > 0 sufficiently small. The proof follows from Kerékjártó’s construction of Brouwer lines for orientation preserving...
S. Dilworth, Maria Girardi, W. Johnson (2000)
Studia Mathematica
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A separable Banach space X contains isomorphically if and only if X has a bounded fundamental total -stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total -biorthogonal system.
Sameer Chavan (2010)
Colloquium Mathematicae
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Let denote a complex, infinite-dimensional, separable Hilbert space, and for any such Hilbert space , let () denote the algebra of bounded linear operators on . We show that for any co-analytic, right-invertible T in (), αT is hypercyclic for every complex α with , where . In particular, every co-analytic, right-invertible T in () is supercyclic.
R. Bittner
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CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions....................................................................................................................................
M. EL Guendafi, M. Mbekhta, E. H. Zerouali (2005)
Banach Center Publications
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Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept...
Oscar Blasco (1988)
Colloquium Mathematicae
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J. M. A. M. van Neerven (2005)
Colloquium Mathematicae
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We give a characterization of uniformly convex Banach spaces in terms of a uniform version of the Kadec-Klee property. As an application we prove that if (xₙ) is a bounded sequence in a uniformly convex Banach space X which is ε-separated for some 0 < ε ≤ 2, then for all norm one vectors x ∈ X there exists a subsequence of (xₙ) such that , where is the modulus of convexity of X. From this we deduce that the unit sphere of every infinite-dimensional uniformly convex Banach space...
R. M. El-Ashwah, M. K. Aouf, S. M. El-Deeb (2011)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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In this paper we introduce and investigate three new subclasses of -valent analytic functions by using the linear operator . The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for -neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.
Takashi Tsuboi (2009)
Annales scientifiques de l'École Normale Supérieure
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The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the -dimensional torus, its identity component is a simple group. For fibered manifolds, for manifolds admitting special semi-free actions and for 2- or 3-dimensional manifolds with nontrivial actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.