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1.
Let H(B) denote the space of all holomorphic functions on the open unit ball B of Cn. Let φ=(φ1,…,φn) be a holomorphic self-map of B and gH(B) such that g(0)=0. In this paper we study the boundedness and compactness of the following integral-type operator, recently introduced by Xiangling Zhu and the second author
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2.
Let A,B,D,E∈[−1,1]. Conditions on A,B,D and E are determined so that
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3.
Let E be a real uniformly convex Banach space whose dual space E satisfies the Kadec-Klee property, K be a closed convex nonempty subset of E. Let be asymptotically nonexpansive mappings of K into E with sequences (respectively) satisfying kin→1 as n→∞, i=1,2,…,m, and . For arbitrary ?∈(0,1), let be a sequence in [?,1−?], for each i∈{1,2,…,m} (respectively). Let {xn} be a sequence generated for m?2 by
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4.
Let E be a real uniformly convex Banach space, K be a closed convex nonempty subset of E which is also a nonexpansive retract with retraction P. Let be asymptotically nonexpansive mappings of K into E with sequences (respectively) satisfying kin→1 as n→∞, i=1,2,…,m, and . Let be a sequence in [?,1−?],?∈(0,1), for each i∈{1,2,…,m} (respectively). Let {xn} be a sequence generated for m?2 by
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5.
6.
Let (Mn,g) be a compact riemannian manifold of dimension n?3. Under some assumptions, we prove that there exists a positive function φ solution of the Yamabe equation
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7.
Given four complex matrices A,B,C and D, where ACn×n and DCm×m, and given a complex number z0: What is the (spectral norm) distance from D to the set of matrices XCm×m such that z0 is a multiple eigenvalue of the matrix
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8.
For 0?σ<1/2 we characterize Carleson measures μ for the analytic Besov-Sobolev spaces on the unit ball Bn in Cn by the discrete tree condition
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9.
Let D be a bounded n-dimensional domain, ∂D be its boundary, be its closure, T be a positive real number, B be an n-dimensional ball {x∈D:|x−b|<R} centered at bD with a radius R, be its closure, ∂B be its boundary, ν denote the unit inward normal at x∂B, and χB(x) be the characteristic function. This article studies the following multi-dimensional parabolic first initial-boundary value problem with a concentrated nonlinear source occupying :
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10.
During the past 10 years multifractal analysis has received an enormous interest. For a sequence n(φn) of functions φn:XM on a metric space X, multifractal analysis refers to the study of the Hausdorff dimension of the level sets
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11.
12.
Let φ be a positive linear functional on Mn(C) and f,g mutually conjugate in the sense of Young. In this note we show a necessary and sufficient condition for the inequality
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13.
In contrast to the famous Henkin-Skoda theorem concerning the zero varieties of holomorphic functions in the Nevanlinna class on the open unit ball Bn in , n?2, it is proved in this article that for any nonnegative, increasing, convex function ?(t) defined on , there exists satisfying such that there is no fHp(Bn), 0<p<∞, with . Here Ng(ζ,1) denotes the integrated zero counting function associated with the slice function gζ. This means that the zero sets of holomorphic functions belonging to the Hardy spaces Hp(Bn), 0<p<∞, unlike that of the holomorphic functions in the Nevanlinna class, cannot be characterized in the above manner.  相似文献   

14.

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Let f(n,m) be the cardinality of largest subset of {1,2,…,n} which does not contain a subset whose elements sum to m. In this note, we show that
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15.
A directed triple system of order v, , is a pair (V,B) where V is a set of v elements and B is a collection of ordered triples of distinct elements of V with the property that every ordered pair of distinct elements of V occurs in exactly one triple as a subsequence. A set of triples in a D is a defining set for D if it occurs in no other on the same set of points. A defining set for D is a smallest defining set for D if D has no defining set of smaller cardinality. In this paper we are interested in the quantity
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16.
Let X={Xt,t?0} be a symmetric Markov process in a state space E and D an open set of E. Denote by XD the subprocess of X killed upon leaving D. Let S={St,t?0} be a subordinator with Laplace exponent φ that is independent of X. The processes Xφ?{XSt,t?0} and are called the subordinate processes of X and XD, respectively. Under some mild conditions, we show that, if {-μn,n?1} and {-λn,n?1} denote the eigenvalues of the generators of the subprocess of Xφ killed upon leaving D and of the process XD respectively, then
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17.
Let X=H/L be an irreducible real bounded symmetric domain realized as a real form in an Hermitian symmetric domain D=G/K. The intersection S of the Shilov boundary of D with X defines a distinguished subset of the topological boundary of X and is invariant under H. It can be realized as S=H/P for certain parabolic subgroup P of H. We study the spherical representations of H induced from P. We find formulas for the spherical functions in terms of the Macdonald hypergeometric function. This generalizes the earlier result of Faraut-Koranyi for Hermitian symmetric spaces D. We consider a class of H-invariant integral intertwining operators from the representations on L2(S) to the holomorphic representations of G restricted to H. We construct a new class of complementary series for the groups H=SO(n,m), SU(n,m) (with nm>2) and Sp(n,m) (with nm>1). We realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of G=SU(n,m), SU(n,mSU(n,m) and SU(2n,2m) respectively.  相似文献   

18.
Let H(B) denote the space of all holomorphic functions on the unit ball B of Cn. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. In this paper, we investigate the boundedness and compactness of the generalized composition operator
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19.
Hao Pan 《Discrete Mathematics》2006,306(16):1921-1940
By a very simple argument, we prove that if l,m,n∈{0,1,2,…} then
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20.
In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))n?0 and (U(n))n?0, which are ultimately periodic modulo m, e.g.
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