共查询到20条相似文献,搜索用时 437 毫秒
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L.D. Abreu F. Marcellan S.B. Yakubovich 《Journal of Mathematical Analysis and Applications》2008,341(2):803-812
Motivated by the G.H. Hardy's 1939 results [G.H. Hardy, Notes on special systems of orthogonal functions II: On functions orthogonal with respect to their own zeros, J. London Math. Soc. 14 (1939) 37-44] on functions orthogonal with respect to their real zeros λn, , we will consider, under the same general conditions imposed by Hardy, functions satisfying an orthogonality with respect to their zeros with Jacobi weights on the interval (0,1), that is, the functions f(z)=zνF(z), ν∈R, where F is entire and
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Jian-Hua Zheng 《Journal of Mathematical Analysis and Applications》2006,313(1):24-37
Let be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f(z) and proved, among others, that if f(z) has a Baker wandering domain U, then for all sufficiently large n, fn(U) contains a round annulus whose module tends to infinity as n→∞ and so for some 0<d<1,
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Let be a positive integer, let F be a family of meromorphic functions in a domain D, all of whose zeros have multiplicity at least k+1, and let , be two holomorphic functions on D. If, for each f∈F, f=a(z)⇔f(k)=h(z), then F is normal in D. 相似文献
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Stephan Ruscheweyh Luis Salinas 《Journal of Mathematical Analysis and Applications》2004,291(2):596-604
An analytic function f(z) in the unit disc D is called stable if sn(f,·)/f?1/f holds for all for . Here sn stands for the nth partial sum of the Taylor expansion about the origin of f, and ? denotes the subordination of analytic functions in . We prove that (1−z)λ, λ∈[−1,1], are stable. The stability of turns out to be equivalent to a famous result of Vietoris on non-negative trigonometric sums. We discuss some generalizations of these results, and related conjectures, always with an eye on applications to positivity results for trigonometric and other polynomials. 相似文献
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S. Ponnusamy A. Vasudevarao 《Journal of Mathematical Analysis and Applications》2007,332(2):1323-1334
Let F1 (F2 respectively) denote the class of analytic functions f in the unit disk |z|<1 with f(0)=0=f′(0)−1 satisfying the condition RePf(z)<3/2 (RePf(z)>−1/2 respectively) in |z|<1, where Pf(z)=1+zf″(z)/f′(z). For any fixed z0 in the unit disk and λ∈[0,1), we shall determine the region of variability for logf′(z0) when f ranges over the class and , respectively. 相似文献
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Róbert Szász László-Róbert Albert 《Journal of Mathematical Analysis and Applications》2007,335(2):1328-1334
A condition for starlikeness will be improved given by the inequality Re(f′(x)+αzf″(z))>0, z∈U, concerning analytic functions of the form f(z)=z+a2z2+? which are defined on the unit disk . 相似文献
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Let k be a positive integer with k?2 and let be a family of functions meromorphic on a domain D in , all of whose poles have multiplicity at least 3, and of whose zeros all have multiplicity at least k+1. Let a(z) be a function holomorphic on D, a(z)?0. Suppose that for each , f(k)(z)≠a(z) for z∈D. Then is a normal family on D. 相似文献
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Qian Lu 《Journal of Mathematical Analysis and Applications》2008,340(1):394-400
We consider the normality criterion for a families F meromorphic in the unit disc Δ, and show that if there exist functions a(z) holomorphic in Δ, a(z)≠1, for each z∈Δ, such that there not only exists a positive number ε0 such that |an(a(z)−1)−1|?ε0 for arbitrary sequence of integers an(n∈N) and for any z∈Δ, but also exists a positive number B>0 such that for every f(z)∈F, B|f′(z)|?|f(z)| whenever f(z)f″(z)−a(z)(f′2(z))=0 in Δ. Then is normal in Δ. 相似文献
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We consider planar differential equations of the form being f(z) and g(z) holomorphic functions and prove that if g(z) is not constant then for any continuum of period orbits the period function has at most one isolated critical period, which is a minimum. Among other implications, the paper extends a well-known result for meromorphic equations, that says that any continuum of periodic orbits has a constant period function. 相似文献
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Haseo Ki 《Journal of Number Theory》2008,128(9):2704-2755
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Let f(z) be a normalized convex (starlike) function on the unit disc D. Let , where z=(z1,z2,…,zn), z1∈D, , pi?1, i=2,…,n, are real numbers. In this note, we prove that Φ(f)(z)=(f(z1),f′(z1)1/p2z2,…,f′(z1)1/pnzn) is a normalized convex (starlike) mapping on Ω, where we choose the power function such that (f′(z1))1/pi|z1=0=1, i=2,…,n. Some other related results are proved. 相似文献
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Stevo Stevi? 《Applied mathematics and computation》2010,215(11):3950-1448
The boundedness of the composition operator Cφf(z)=f(φ(z)) from the Hardy space , where X is the upper half-plane or the unit disk D={z∈C:|z|<1} in the complex plane C, to the nth weighted-type space, where φ is an analytic self-map of X, is characterized. 相似文献
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Kenji Kimura 《Discrete Mathematics》2006,306(6):607-611
A relationship is considered between an f-factor of a graph and that of its vertex-deleted subgraphs. Katerinis [Some results on the existence of 2n-factors in terms of vertex-deleted subgraphs, Ars Combin. 16 (1983) 271-277] proved that for even integer k, if G-x has a k-factor for each x∈V(G), then G has a k-factor. Enomoto and Tokuda [Complete-factors and f-factors, Discrete Math. 220 (2000) 239-242] generalized Katerinis’ result to f-factors, and proved that if G-x has an f-factor for each x∈V(G), then G has an f-factor for an integer-valued function f defined on V(G) with even. In this paper, we consider a similar problem to that of Enomoto and Tokuda, where for several vertices x we do not have to know whether G-x has an f-factor. Let G be a graph, X be a set of vertices, and let f be an integer-valued function defined on V(G) with even, |V(G)-X|?2. We prove that if and if G-x has an f-factor for each x∈V(G)-X, then G has an f-factor. Moreover, if G excludes an isolated vertex, then we can replace the condition with . Furthermore the condition will be when |X|=1. 相似文献
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Hidetaka Hamada Tatsuhiro Honda Gabriela Kohr 《Journal of Mathematical Analysis and Applications》2006,317(1):302-319
Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in . 相似文献