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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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.
M. K. Aouf (1989)
Matematički Vesnik
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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....................................................................................................................................
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...
J. Siciak (1969)
Annales Polonici Mathematici
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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.
Wilhelmina Smajdor (1970)
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...
Wolfgang Tutschke (1983)
Banach Center Publications
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Tobias Heinrich (2005)
Annales Polonici Mathematici
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For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition it is shown that for each real simple curve γ and each d ≥ 1 the limit variety satisfies the strong Phragmén-Lindelöf condition (SPL).
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.
Klas Diederich, Emmanuel Mazzilli (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Let be a closed real-analytic subset and put This article deals with the question of the structure of . In the main result a natural proof is given for the fact, that always is closed. As a main tool an interesting relation between complex analytic subsets of of positive dimension and the Segre varieties of is proved and exploited.
Jagannath Patel, Ashok Kumar Sahoo (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass of and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.
Sönke Blunck (2000)
Colloquium Mathematicae
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In analogy to the analyticity condition , t > 0, for a continuous time semigroup , a bounded operator T is called analytic if the discrete time semigroup satisfies , n ∈ ℕ. We generalize O. Nevanlinna’s characterization of powerbounded and analytic operators T to the following perturbation result: if S is a perturbation of T such that is small enough for some , then the type of the semigroup also controls the analyticity of S in the sense that , n ∈ ℕ. As an application...
S. Achimescu, V. Alexandru, N. Popescu, M. Vâjâitu, A. Zaharescu (2012)
Rendiconti del Seminario Matematico della Università di Padova
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Mami Suzuki (2011)
Annales Polonici Mathematici
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For nonlinear difference equations, it is difficult to obtain analytic solutions, especially when all the eigenvalues of the equation are of absolute value 1. We consider a second order nonlinear difference equation which can be transformed into the following simultaneous system of nonlinear difference equations: ⎧ x(t+1) = X(x(t),y(t)) ⎨ ⎩ y(t+1) = Y(x(t), y(t)) where , satisfy some conditions. For these equations, we have obtained analytic solutions in the cases "|λ₁| ≠ 1 or |λ₂|...