共查询到20条相似文献,搜索用时 31 毫秒
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Sophie Grivaux 《Comptes Rendus Mathematique》2010,348(3-4):155-159
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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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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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The edit distance problem for rooted unordered trees is known to be NP-hard. Based on this fact, this paper studies exponential-time algorithms for the problem. For a general case, an time algorithm is presented, where and are the numbers of nodes and and are the numbers of branching nodes in two input trees. This algorithm is obtained by a combination of dynamic programming, exhaustive search, and maximum weighted bipartite matching. For bounded degree trees over a fixed alphabet, it is shown that the problem can be solved in time for any fixed . This result is achieved by avoiding duplicate calculations for identical subsets of small subtrees. 相似文献
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Soyeun Jung 《Journal of Differential Equations》2012,253(6):1807-1861
By working with the periodic resolvent kernel and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction–diffusion equations. With our linearized estimates together with a nonlinear iteration scheme developed by Johnson–Zumbrun, we obtain -behavior () of a nonlinear solution to a perturbation equation of a reaction–diffusion equation with respect to initial data in recovering and slightly sharpening results obtained by Schneider using weighted energy and renormalization techniques. We obtain also pointwise nonlinear estimates with respect to two different initial perturbations , and , , respectively, sufficiently small and sufficiently large, showing that behavior is that of a heat kernel. These pointwise bounds have not been obtained elsewhere, and do not appear to be accessible by previous techniques. 相似文献
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Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
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This paper deals with the following nonlinear elliptic equation where , is a bounded non-negative function in . By combining a finite reduction argument and local Pohozaev type of identities, we prove that if and has a stable critical point with and , then the above problem has infinitely many solutions. This paper overcomes the difficulty appearing in using the standard reduction method to locate the concentrating points of the solutions. 相似文献
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In this paper, we study operator-theoretic properties of the compressed shift operators and on complements of submodules of the Hardy space over the bidisk . Specifically, we study Beurling-type submodules – namely submodules of the form for θ inner – using properties of Agler decompositions of θ to deduce properties of and on model spaces . Results include characterizations (in terms of θ) of when a commutator has rank n and when subspaces associated to Agler decompositions are reducing for and . We include several open questions. 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