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M. Gürdal 《Expositiones Mathematicae》2009,27(2):153-160
In the present paper we consider the Volterra integration operator V on the Wiener algebra W(D) of analytic functions on the unit disc D of the complex plane C. A complex number λ is called an extended eigenvalue of V if there exists a nonzero operator A satisfying the equation AV=λVA. We prove that the set of all extended eigenvalues of V is precisely the set C?{0}, and describe in terms of Duhamel operators and composition operators the set of corresponding extended eigenvectors of V. The similar result for some weighted shift operator on ?p spaces is also obtained. 相似文献
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It is proved that for each prime field GF(p), there is an integer np such that a 4-connected matroid has at most np inequivalent representations over GF(p). We also prove a stronger theorem that obtains the same conclusion for matroids satisfying a connectivity condition, intermediate between 3-connectivity and 4-connectivity that we term “k-coherence”. 相似文献
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For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞?[an(Cφ)]1/n=e−1/Cap[φ(D)], where Cap[φ(D)] is the Green capacity of φ(D) in D. This formula holds also for Hp with 1≤p<∞. 相似文献
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We show that for each p∈(0,1] there exists a separable p -Banach space Gp of almost universal disposition, that is, having the following extension property: for each ε>0 and each isometric embedding g:X→Y, where Y is a finite-dimensional p-Banach space and X is a subspace of Gp, there is an ε -isometry f:Y→Gp such that x=f(g(x)) for all x∈X. 相似文献
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In this paper, we give some Liouville-type theorems for Lp(p∈R) harmonic (resp. subharmonic, superharmonic) functions on forward complete Finsler manifolds. Moreover, we derive a gradient estimate for harmonic functions on a closed Finsler manifold. As an application, one obtains that any harmonic function on a closed Finsler manifold with nonnegative weighted Ricci curvature RicN(N∈(n,∞)) must be constant. 相似文献
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Let F be an algebraically closed field. Let V be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form B over F. Suppose the characteristic of F is sufficiently large , i.e. either zero or greater than the dimension of V. Let I(V,B) denote the group of isometries. Using the Jacobson–Morozov lemma we give a new and simple proof of the fact that two elements in I(V,B) are conjugate if and only if they have the same elementary divisors. 相似文献
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Michael Aristidou Mark Davidson Gestur Ólafsson 《Journal of Computational and Applied Mathematics》2007
In this article we derive differential recursion relations for the Laguerre functions on the cone Ω of positive definite real matrices. The highest weight representations of the group Sp(n,R) play a fundamental role. Each such representation acts on a Hilbert space of holomorphic functions on the tube domain Ω+iSym(n,R). We then use the Laplace transform to carry the Lie algebra action over to L2(Ω,dμν). The differential recursion relations result by restricting to a distinguished three-dimensional subalgebra, which is isomorphic to sl(2,R). 相似文献