共查询到20条相似文献,搜索用时 46 毫秒
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《Discrete Mathematics》2006,306(10-11):973-978
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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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Fritz Gesztesy Lance L. Littlejohn Isaac Michael Richard Wellman 《Journal of Differential Equations》2018,264(4):2761-2801
In 1961, Birman proved a sequence of inequalities , for , valid for functions in . In particular, is the classical (integral) Hardy inequality and is the well-known Rellich inequality. In this paper, we give a proof of this sequence of inequalities valid on a certain Hilbert space of functions defined on . Moreover, implies ; as a consequence of this inclusion, we see that the classical Hardy inequality implies each of the inequalities in Birman's sequence. We also show that for any finite , these inequalities hold on the standard Sobolev space . Furthermore, in all cases, the Birman constants in these inequalities are sharp and the only function that gives equality in any of these inequalities is the trivial function in (resp., ). We also show that these Birman constants are related to the norm of a generalized continuous Cesàro averaging operator whose spectral properties we determine in detail. 相似文献
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A. Jänig 《Journal of Differential Equations》2018,264(9):5713-5733
We consider asymptotically autonomous semilinear parabolic equations Suppose that as , where the semiflows induced by
(*)
are gradient-like. Under certain assumptions, it is shown that generically with respect to a perturbation g with as , every solution of is a connection between equilibria of (*) with . Moreover, if the Morse indices satisfy , then u is isolated by linearization. 相似文献
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Payman Eskandari 《Comptes Rendus Mathematique》2018,356(3):312-315
Let X be a Riemann surface of positive genus. Denote by the configuration space of n distinct points on X. We use the Betti–de Rham comparison isomorphism on to define an integrable connection on the trivial vector bundle on with fiber the universal algebra of the Lie algebra associated with the descending central series of of . The construction is inspired by the Knizhnik–Zamolodchikov system in genus zero and its integrability follows from Riemann period relations. 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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《Stochastic Processes and their Applications》2005,115(2):275-298
In this paper, we consider a uniformly ergodic Markov process valued in a measurable subset E of with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in and for , and the asymptotic optimality in the Bahadur sense. These generalize the known results in the i.i.d. case. 相似文献