منابع مشابه
Analytic Functions and Boundary Values
Analytic functions in tubes T B = R+iB in C, where B 1⁄2 R, that generalize the Hardy H spaces are studied. The associated function M¤ of Komatsu, which is de ̄ned with the aid of certain sequences of positive real numbers, is involved in the generalizing bound of the L norm. Fourier-Laplace and Cauchy integral representations are obtained for these functions. These representations can be used t...
متن کاملBoundary Values of Continuous Analytic Functions
Let U, K, and C denote the open unit disc, the closed unit disc, and the unit circumference, respectively. Let A be the set of all complex-valued functions which are defined and continuous on K and analytic in U. The theorem proved in this paper states that if £ is a closed subset of C, of (Lebesgue) measure zero, and if <p is a continuous function defined on £, then there exists a function /£....
متن کاملOn a boundary property of analytic functions
Let f be an analytic function in the unit disc [Formula: see text] on the complex plane [Formula: see text]. This paper is devoted to obtaining the correspondence between [Formula: see text] and [Formula: see text] at the point w, [Formula: see text], such that [Formula: see text]. We present several applications of the main result. A part of them improve the previous results of this type.
متن کاملRigidity of Analytic Functions at the Boundary
then f(z) = z. We will refer to this theorem as Burns-Krantz theorem. The Burns-Krantz theorem was generalized to finite Blaschke products by D. Chelst [3]. The proof of both Burns-Krantz theorem and the that of the theorem of Chelst uses Hopf lemma. In a recent paper, [1], L. Baracco, D.Zaitsev and G. Zampieri gave a new and elementary proof for the Burns-Krantz theorem ([1, proposition 3.1.])...
متن کاملOn Certain Analytic Functions of Bounded Boundary Rotation
In this paper we introduce certain analytic functions of boundary rotation bounded by k1r which are of Caratheodory origin. With them we study two classes of analytic and univalent functions in the unit disk E = {z E C Izi < I} , which are also of bounded boundary rotation.
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ژورنال
عنوان ژورنال: Analysis and Mathematical Physics
سال: 2014
ISSN: 1664-2368,1664-235X
DOI: 10.1007/s13324-014-0074-0