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We give a full characterization of smooth symbols ψ:R→R for which the composition operator Cψ:C∞(R)→C∞(R), F?F°ψ has closed range. This generalizes in a special case the result of Kenessey and Wengenroth who gave such a characterization for smooth injective symbols ψ:R→Rd. 相似文献
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We find some sufficient conditions for a system of partial derivatives of an entire function to be complete in the space H(Cd) of all entire functions of d variables. As an application of this result we describe new classes of frequently hypercyclic operators on H(Cd). 相似文献
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Mohamed Ali Toumi 《Expositiones Mathematicae》2010,28(3):269-275
Let A be an Archimedean f -algebra and let N(A) be the set of all nilpotent elements of A. Colville et al. [4] proved that a positive linear map d:A→A is a derivation if and only if d(A)⊂N(A) and d(A2)={0}, where A2 is the set of all products ab in A. 相似文献
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The paper aims to investigate the convergence of the q -Bernstein polynomials Bn,q(f;x) attached to rational functions in the case q>1. The problem reduces to that for the partial fractions (x−α)−j, j∈N. The already available results deal with cases, where either the pole α is simple or α≠q−m, m∈N0. Consequently, the present work is focused on the polynomials Bn,q(f;x) for the functions of the form f(x)=(x−q−m)−j with j?2. For such functions, it is proved that the interval of convergence of {Bn,q(f;x)} depends not only on the location, but also on the multiplicity of the pole – a phenomenon which has not been considered previously. 相似文献
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In this article we apply a recently established transference principle in order to obtain the boundedness of certain functional calculi for semigroup generators. In particular, it is proved that if −A generates a C0-semigroup on a Hilbert space, then for each τ>0 the operator A has a bounded calculus for the closed ideal of bounded holomorphic functions on a (sufficiently large) right half-plane that satisfy f(z)=O(e−τRe(z)) as |z|→∞. The bound of this calculus grows at most logarithmically as τ↘0. As a consequence, f(A) is a bounded operator for each holomorphic function f (on a right half-plane) with polynomial decay at ∞. Then we show that each semigroup generator has a so-called (strong) m -bounded calculus for all m∈N, and that this property characterizes semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called γ-bounded semigroups, the Hilbert space results actually hold in general Banach spaces. 相似文献
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This paper treats some variational principles for solutions of inhomogeneous p -Laplacian boundary value problems on exterior regions U?RN with dimension N?3. Existence-uniqueness results when p∈(1,N) are provided in a space E1,p(U) of functions that contains W1,p(U). Functions in E1,p(U) are required to decay at infinity in a measure theoretic sense. Various properties of this space are derived, including results about equivalent norms, traces and an Lp-imbedding theorem. Also an existence result for a general variational problem of this type is obtained. 相似文献
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Let K be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L∞(K) and C0(K), the class of left translation invariant w?-subalgebras of L∞(K) and finally the class of non-zero left translation invariant C?-subalgebras of C0(K) in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w?-subalgebras of L∞(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C?-subalgebras of C0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L∞(K) and C0(K). 相似文献
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Let R=(-∞,∞) and let Q∈C2:R→R+=[0,∞) be an even function. Then in this paper we consider the infinite–finite range inequality, an estimate for the Christoffel function, and the Markov–Bernstein inequality with the exponential weights wρ(x)=|x|ρe-Q(x),x∈R. 相似文献
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We study the existence of solutions u:R3→R2 for the semilinear elliptic systems where W:R2→R is a double well symmetric potential. We use variational methods to show, under generic non-degenerate properties of the set of one dimensional heteroclinic connections between the two minima a± of W, that (0.1) has infinitely many geometrically distinct solutions u∈C2(R3,R2) which satisfy u(x,y,z)→a± as x→±∞ uniformly with respect to (y,z)∈R2 and which exhibit dihedral symmetries with respect to the variables y and z . We also characterize the asymptotic behavior of these solutions as |(y,z)|→+∞. 相似文献
equation(0.1)
−Δu(x,y,z)+∇W(u(x,y,z))=0,
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This study is devoted to analysis of semi-implicit compact finite difference (SICFD) methods for the nonlinear Schrödinger equation (NLS) perturbed by the wave operator (NLSW) with a perturbation strength described by a dimensionless parameter ε∈(0,1]. Uniform l∞-norm error bounds of the proposed SICFD schemes are built to give immediate insight on point-wise error occurring as time increases, and the explicit dependence of the mesh size and time step on the parameter ε is also figured out. In the small ε regime, highly oscillations arise in time with O(ε2)-wavelength. This highly oscillatory nature in time as well as the difficulty raised by the compact FD discretization make establishing the l∞-norm error bounds uniformly in ε of the SICFD methods for NLSW to be a very interesting and challenging issue. The uniform l∞-norm error bounds in ε are proved to be of O(h4+τ) and O(h4+τ2/3) with time step τ and mesh size h for well-prepared and ill-prepared initial data. Finally, numerical results are reported to verify the error estimates and show the sharpness of the convergence rates in the respectively parameter regimes. 相似文献