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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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The L resolvents of second-order elliptic operators of divergence form under the Dirichlet condition
Yoichi Miyazaki 《Journal of Differential Equations》2004,206(2):353-372
Let A be the 2mth-order elliptic operator of divergence form with bounded measurable coefficients defined in a domain Ω of . For 1<p<∞ we regard A as a bounded linear operator from the Lp Sobolev space to H−m,p(Ω). It is known that when , we can construct the resolvent (A−λ)−1 and estimate its operator norm for some λ if the leading coefficients are uniformly continuous. In this paper, we try to extend this result to a general domain. It is successful when m=1 if Ω is the half-space or a domain with C2 bounded boundary. For m>1 it is shown that the problem is reduced to the case where Ω is the half-space and A is a homogeneous operator with constant coefficients. We also give a perturbation theorem. 相似文献
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Let s∈R, τ∈[0,∞), p∈(1,∞) and q∈(1,∞]. In this paper, we introduce a new class of function spaces which unify and generalize the Triebel-Lizorkin spaces with both p∈(1,∞) and p=∞ and Q spaces. By establishing the Carleson measure characterization of Q space, we then determine the relationship between Triebel-Lizorkin spaces and Q spaces, which answers a question posed by Dafni and Xiao in [G. Dafni, J. Xiao, Some new tent spaces and duality theorem for fractional Carleson measures and Qα(Rn), J. Funct. Anal. 208 (2004) 377-422]. Moreover, via the Hausdorff capacity, we introduce a new class of tent spaces and determine their dual spaces , where s∈R, p,q∈[1,∞), max{p,q}>1, , and t′ denotes the conjugate index of t∈(1,∞); as an application of this, we further introduce certain Hardy-Hausdorff spaces and prove that the dual space of is just when p,q∈(1,∞). 相似文献
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Chun-Gil Park 《Journal of Mathematical Analysis and Applications》2005,307(2):753-762
It is shown that every almost linear bijection of a unital C∗-algebra A onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all unitaries u∈A, all y∈A, and n=0,1,2,…, and that almost linear continuous bijection of a unital C∗-algebra A of real rank zero onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all , all y∈A, and n=0,1,2,…. Assume that X and Y are left normed modules over a unital C∗-algebra A. It is shown that every surjective isometry , satisfying T(0)=0 and T(ux)=uT(x) for all x∈X and all unitaries u∈A, is an A-linear isomorphism. This is applied to investigate C∗-algebra isomorphisms between unital C∗-algebras. 相似文献
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Let H be the real quaternion algebra and Hn×m denote the set of all n×m matrices over H. Let P∈Hn×n and Q∈Hm×m be involutions, i.e., P2=I,Q2=I. A matrix A∈Hn×m is said to be (P,Q)-symmetric if A=PAQ. This paper studies the system of linear real quaternion matrix equations
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A consecutive(r, s)-out-of-(m, n):F lattice system which is defined as a two-dimensional version of a consecutive k-out-of-n:F system is used as a reliability evaluation model for a sensor system, an X-ray diagnostic system, a pattern search system, etc. This system consists of m × n components arranged like an (m, n) matrix and fails iff the system has an (r, s) submatrix that contains all failed components. In this paper we deal a combined model of a k-out-of-mn:F and a consecutive (r, s)-out-of-(m, n):F lattice system. Namely, the system has one more condition of system down, that is the total number of failed components, in addition to that of a consecutive (r, s)-out-of-(m, n):F lattice system. We present a method to obtain reliability of the system. The proposed method obtains the reliability by using a combinatorial equation that does not depend on the system size. Some numerical examples are presented to show the relationship between component reliability and system reliability. 相似文献
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In this paper we consider the generalized Marcum Q-function of order ν > 0 real, defined by
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Houria Triki 《Applied mathematics and computation》2010,217(4):1733-9479
We consider the nonlinear dispersive K(m,n) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sechp function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K(m,n) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K(m,n) equations in the presence of the generalized evolution term. An extended form of the K(m,n) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K(m,n) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. 相似文献
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Antoine Derighetti 《Journal of Functional Analysis》2004,215(2):341-365
Let G be a locally compact group and let p∈(1,∞). Let be any of the Banach spaces Cδ,p(G), PFp(G), Mp(G), APp(G), WAPp(G), UCp(G), PMp(G), of convolution operators on Lp(G). It is shown that PFp(G)′ can be isometrically embedded into UCp(G)′. The structure of maximal regular ideals of (and of MAp(G)″, Bp(G)″, Wp(G)″) is studied. Among other things it is shown that every maximal regular left (right, two sided) ideal in is either dense or is the annihilator of a unique element in the spectrum of Ap(G). Minimal ideals of is also studied. It is shown that a left ideal M in is minimal if and only if , where Ψ is either a right annihilator of or is a topologically x-invariant element (for some x∈G). Some results on minimal right ideals are also given. 相似文献
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A (d,1)-total labelling of a graph G assigns integers to the vertices and edges of G such that adjacent vertices receive distinct labels, adjacent edges receive distinct labels, and a vertex and its incident edges receive labels that differ in absolute value by at least d. The span of a (d,1)-total labelling is the maximum difference between two labels. The (d,1)-total number, denoted , is defined to be the least span among all (d,1)-total labellings of G. We prove new upper bounds for , compute some for complete bipartite graphs Km,n, and completely determine all for d=1,2,3. We also propose a conjecture on an upper bound for in terms of the chromatic number and the chromatic index of G. 相似文献
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This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem
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Zhihua Ren 《Journal of Mathematical Analysis and Applications》2003,284(1):118-126
In this paper we study smooth classification of hyperbolic vector fields based on their linear approximations only and obtain the following. On Rn, n?5, with only two kinds of exceptions, any two hyperbolic vector fields with generic nonlinear parts and where Ai are n×n matrices, are C1 conjugate to each other if and only if A1 and A2 are strictly similar, and they are C1 orbitally equivalent if and only if A1 and A2 are similar. 相似文献
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Until now the concept of a Soules basis matrix of sign patternN consisted of an orthogonal matrix R∈Rn,n, generated in a certain way from a positive n-vector, which has the property that for any diagonal matrix Λ = diag(λ1, … , λn), with λ1 ? ? ? λn ? 0, the symmetric matrix A = RΛRT has nonnegative entries only. In the present paper we introduce the notion of a pair of double Soules basis matrices of sign patternN which is a pair of matrices (P, Q), each in Rn,n, which are not necessarily orthogonal and which are generated in a certain way from two positive vectors, but such that PQT = I and such that for any of the aforementioned diagonal matrices Λ, the matrix A = PΛQT (also) has nonnegative entries only. We investigate the interesting properties which such matrices A have.As a preamble to the above investigation we show that the iterates, , generated in the course of the QR-algorithm when it is applied to A = RΛRT, where R is a Soules basis matrix of sign pattern N, are again symmetric matrices generated by the Soules basis matrices Rk of sign pattern N which are themselves modified as the algorithm progresses.Our work here extends earlier works by Soules and Elsner et al. 相似文献