共查询到20条相似文献,搜索用时 62 毫秒
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In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(D~n, B~N) is C~(1+α) at z0 ∈ E_rD~n with f(0) = 0 and f(z_0) = ω_0∈B~N for any n,N ≥ 1, then there exist a nonnegative vector λ_f =(λ_1,0,…,λ_r,0,…,0)~T∈R~(2 n)satisfying λ_i≥1/(2~(2 n-1)) for 1 ≤ i ≤ r such that where z'_0 and w'_0 are real versions of z_0 and w_0, respectively. 相似文献
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Stephan Fackler 《Comptes Rendus Mathematique》2013,351(1-2):53-56
In this short Note we give a self-contained example of a consistent family of holomorphic semigroups such that does not have maximal regularity for . This answers negatively the open question whether maximal regularity extrapolates from to the -scale. 相似文献
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Włodzimierz Wysocki 《Statistics & probability letters》2012,82(4):818-826
We introduce a family of functions called diagonal generators. These are convex functions with the properties of diagonal sections of archimedean copulas. We show that to each diagonal generator there corresponds an archimedean copula with the asymptotic representation . Moreover, the diagonal section of equals .We characterize archimedean copulas in terms of their asymptotic form. We construct a family of diagonal generators, induced by a regular distribution function . We study a differential equation (depending on a function parameter), whose solution is . We give four applications of diagonal generators: to concordance, quadrant dependence, measures of dependence and convergence of copulas. 相似文献
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We consider the system of nonlinear wave equations with initial and Dirichlet boundary conditions. Under some suitable assumptions on the functions, , , , parameters and the initial data, the result on blow-up of solutions and upper bound of blow-up time are given. 相似文献
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Vladimir Bolotnikov 《Journal of Approximation Theory》2011,163(4):568-589
Characterization of Schur-class functions (analytic and bounded by one in modulus on the open unit disk) in terms of their Taylor coefficients at the origin is due to I. Schur. We present a boundary analog of this result: necessary and sufficient conditions are given for the existence of a Schur-class function with the prescribed nontangential boundary expansion at a given point on the unit circle. 相似文献
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Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
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Nguyen Van THIN 《数学物理学报(B辑英文版)》2017,37(3):623-656
In 1996, C. C. Yang and P. C. Hu [8] showed that: Let f be a transcendental meromorphic function on the complex plane, and a = 0 be a complex number; then assume that n ≥ 2, n_1, ···, n_k are nonnegative integers such that n_1+ ··· + n_k ≥1; thus f~n(f′)~(n_1)···(f~(k))~(n_k)-a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥ 2. Namely, we prove that f~n(f′)~(n_1)···(f~(k))~(n_k)-a(z)has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k ≥ 2, and a(z) ≡ 0 is a small function of f and n ≥ 2, n_1, ···, n_k are nonnegative integers satisfying n1+ ··· + n k ≥1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by J. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y.Xu [10]. The main result of this article also leads to a counterexample to the converse of Bloch's principle. 相似文献