共查询到20条相似文献,搜索用时 15 毫秒
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Alexander Yu. Solynin 《Proceedings of the American Mathematical Society》2008,136(2):577-585
Let be analytic on the unit disk with . In 1989, D. Marshall conjectured the existence of the universal constant such that whenever the area, counting multiplicity, of a portion of over is . Recently, P. Poggi-Corradini (2007) proved this conjecture with an unspecified constant by the method of extremal metrics. In this note we show that such a universal constant exists for a much larger class consisting of analytic functions omitting two values of a certain doubly-sheeted Riemann surface. We also find a numerical value, , which is sharp for the problem in this larger class but is not sharp for Marshall's problem.
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Aequationes mathematicae - 相似文献
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V. V. Lebedev 《Functional Analysis and Its Applications》2014,48(3):231-234
We consider bounded analytic functions in domains generated by sets with the Littlewood-Paley property. We show that each such function is an l p -multiplier. 相似文献
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M. M. Sheremeta 《Journal of Mathematical Sciences》1999,96(2):2988-2994
We establish conditions on an increasing sequence (np) of nonnegative integers that guarantee that a functionf analytic in the unit disk {z ¦z¦< 1} can be analytically continued to a disk of larger radius provided all of its derivatives
are univalent in the disk.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 58–65. 相似文献
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Ian N. Deters Steven M. Seubert 《Journal of Mathematical Analysis and Applications》2007,334(2):1209-1219
The purpose of this paper is to study cyclic vectors and invariant subspaces of operators on the space of functions analytic on an open disk in the complex plane having as eigenvectors the monomials zn. 相似文献
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E. G. Kir’yatskiĭ 《Siberian Mathematical Journal》2011,52(6):1009-1021
We estimate the absolute value and real part of the order n divided difference of an analytic function on a disk. Particular attention in these estimates is paid to the question of
equality. 相似文献
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Analogs of the classical theorems of Liouville, Phragmén-Lindelöf, and Paley-Wiener are proved in the class of discrete analytic functions. 相似文献
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R. B. Salimov 《Russian Mathematics (Iz VUZ)》2012,56(3):36-44
We obtain representations for an analytic in a disc function such that its real part has a zero of an integer order at a fixed
boundary point. We consider certain applications of these representations for studying properties of singular integrals with
Hilbert kernel. 相似文献
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Richard Fournier Stephan Ruscheweyh 《Proceedings of the American Mathematical Society》1999,127(11):3287-3294
We shall prove (a slightly more general version of) the following theorem: let be analytic in the closed unit disk with , and let be a finite Blaschke product. Then there exists a function satisfying: i) analytic in the closed unit disk , ii) , iii) in , such that
. For these important choices of we also prove that the corresponding functions are uniquely determined by , and that is univalent in . Our work is related to Beurling's and Avhadiev's on conformal mappings solving free boundary value conditions in the unit disk.
satisfies
This completes a recent result of Kühnau for , , where this boundary value problem has a geometrical interpretation, namely that preserves hyperbolic arc length on for suitable
. For these important choices of we also prove that the corresponding functions are uniquely determined by , and that is univalent in . Our work is related to Beurling's and Avhadiev's on conformal mappings solving free boundary value conditions in the unit disk.
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A. A. Pekarskii 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):215-220
Denote by C A the set of functions that are analytic in the disk |z| < 1 and continuous on its closure |z| ≤ 1; let ? n , n = 0, 1, 2, ..., be the set of rational functions of degree at most n. Denote by R n (f) (R n (f) A ) the best uniform approximation of a function f ∈ C A on the circle |z| = 1 (in the disk |z| ≤ 1) by the set ? n . The following equality is proved for any n ≥ 1: sup{R n (f) A /R n (f): f ∈ C A ? ? n } = 2. We also consider a similar problem of comparing the best approximations of functions in C A by polynomials and trigonometric polynomials. 相似文献
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Li-Mei Wang 《Journal of Mathematical Analysis and Applications》2022,505(1):125448
In this paper, the order of convexity of is given under certain conditions on the positive real parameters a, b and c. We show also that the image domains of the unit disc under some shifted zero-balanced hypergeometric functions are convex and bounded by two horizontal lines. This solves a problem raised by Ponnusamy and Vuorinen in [10]. 相似文献