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1.
In this paper, the authors give a counterexample to show that the classical dyadic Hausdorff capacity on Rn when n?2 and 0<d?n−1 is not a capacity in the sense of Choquet. A variant of the classical dyadic Hausdorff capacity, , is then introduced and is further proved to be a capacity in the sense of Choquet. 相似文献
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Hartmut Pecher 《Journal of Mathematical Analysis and Applications》2008,342(2):1440-1454
The 1D Cauchy problem for the Zakharov system is shown to be locally well-posed for low regularity Schrödinger data and wave data under certain assumptions on the parameters k,l and 1<p?2, where , generalizing the results for p=2 by Ginibre, Tsutsumi and Velo. Especially we are able to improve the results from the scaling point of view, and also allow suitable k<0, l<−1/2, i.e. data u0∉L2 and (n0,n1)∉H−1/2×H−3/2, which was excluded in the case p=2. 相似文献
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For Jacobi matrices with an=1+(−1)nαn−γ, bn=(−1)nβn−γ, we study bound states and the Szeg? condition. We provide a new proof of Nevai's result that if , the Szeg? condition holds, which works also if one replaces (−1)n by . We show that if α=0, β≠0, and , the Szeg? condition fails. We also show that if γ=1, α and β are small enough ( will do), then the Jacobi matrix has finitely many bound states (for α=0, β large, it has infinitely many). 相似文献
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Vladimir Petrov Kostov 《Bulletin des Sciences Mathématiques》2005,129(9):775-781
A polynomial-like function (PLF) of degree n is a smooth function F whose nth derivative never vanishes. A PLF has ?n real zeros; in case of equality it is called hyperbolic; F(i) has ?n−i real zeros. We consider the arrangements of the n(n+1)/2 distinct real numbers , i=0,…,n−1, k=1,…,n−i, which satisfy the conditions . We ask the question whether all such arrangements are realizable by the roots of a hyperbolic PLF and its derivatives. We show that for n?5 the answer is negative. 相似文献
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Hua Wang 《Journal of Mathematical Analysis and Applications》2011,381(1):134-145
In this paper, by using the atomic decomposition and molecular characterization of the homogeneous and non-homogeneous weighted Herz-type Hardy spaces , we obtain some weighted boundedness properties of the Bochner-Riesz operator and the maximal Bochner-Riesz operator on these spaces for α=n(1/p−1/q), 0<p?1 and 1<q<∞. 相似文献
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Let −D<−4 denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of exists. Let d be a fundamental discriminant prime to D. Let 2k−1 be an odd natural number prime to the class number of . Let χ be the twist of the (2k−1)th power of a canonical Hecke character of by the Kronecker's symbol . It is proved that the vanishing order of the Hecke L-function L(s,χ) at its central point s=k is determined by its root number when , where the constant implied in the symbol ? depends only on k and ?, and is effective for L-functions with root number −1. 相似文献
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Ming-Yi Lee 《Journal of Mathematical Analysis and Applications》2006,324(2):1274-1281
Let w be a Muckenhoupt weight and be the weighted Hardy spaces. We use the atomic decomposition of and their molecular characters to show that the Bochner-Riesz means are bounded on for 0<p?1 and δ>max{n/p−(n+1)/2,[n/p]rw−1(rw−1)−(n+1)/2}, where rw is the critical index of w for the reverse Hölder condition. We also prove the boundedness of the maximal Bochner-Riesz means for 0<p?1 and δ>n/p−(n+1)/2. 相似文献
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Vladimir Petrov Kostov 《Bulletin des Sciences Mathématiques》2007,131(5):477
A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P(n) vanishes nowhere. Denote by the roots of P(i), k=1,…,n−i, i=0,…,n−1. Then in the absence of any equality of the form one has ∀i<j, (the Rolle theorem). For n?4 (resp. for n?5) not all arrangements without equalities (∗) of n(n+1)/2 real numbers and compatible with (∗∗) (we call them admissible) are realizable by the roots of hyperbolic polynomials (resp. of HPLFs) of degree n and of their derivatives. For n=5 we show that from 286 admissible arrangements, exactly 236 are realizable by HPLFs; from these 236 arrangements, 116 are realizable by hyperbolic polynomials and 24 by perturbations of such. 相似文献
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Marco Franciosi 《Advances in Mathematics》2004,186(2):317-333
Let C be a numerically connected curve lying on a smooth algebraic surface. We show that if is an ample invertible sheaf satisfying some technical numerical hypotheses then is normally generated. As a corollary we show that the sheaf ωC⊗2 on a numerically connected curve C of arithmetic genus pa?3 is normally generated if ωC is ample and does not exist a subcurve B⊂C such that pa(B)=1=B(C−B). 相似文献
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We find lower bounds on the difference between the spectral radius λ1 and the average degree of an irregular graph G of order n and size e. In particular, we show that, if n ? 4, then
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Yuan Zhou 《Journal of Mathematical Analysis and Applications》2011,382(2):577-593
The author establishes some geometric criteria for a Haj?asz-Sobolev -extension (resp. -imbedding) domain of Rn with n?2, s∈(0,1] and p∈[n/s,∞] (resp. p∈(n/s,∞]). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α-cigar domain with α∈(0,1) if and only if for some/all s∈[α,1) and p=(2−α)/(s−α), where denotes the restriction of the Triebel-Lizorkin space on Ω. 相似文献
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A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations
Cristian Rios 《Advances in Mathematics》2005,193(2):373-415
In dimension n?3, we define a generalization of the classical two-dimensional partial Legendre transform, that reduces interior regularity of the generalized Monge-Ampère equation to regularity of a divergence form quasilinear system of special form. This is then used to obtain smoothness of C2,1 solutions, having n-1 nonvanishing principal curvatures, to certain subelliptic Monge-Ampère equations in dimension n?3. A corollary is that if k?0 vanishes only at nondegenerate critical points, then a C2,1 convex solution u is smooth if and only if the symmetric function of degree n-1 of the principal curvatures of u is positive, and moreover, u fails to be when not smooth. 相似文献
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Wolfgang Reichel 《Journal of Mathematical Analysis and Applications》2003,287(1):75-89
We continue Part I of this paper on polyharmonic boundary value problems (−Δ)mu=f(u) on , , with Dirichlet boundary conditions. Here Ω is a bounded or unbounded conformally contractible domain as defined in Part I. The uniqueness principle proved in Part I is applied to show the following theorems: if f(s)=λs+|s|p−1s, λ?0, with a supercritical p>(n+2m)/(n−2m) we extend the well-known non-existence result of Pucci and Serrin (Indiana Univ. Math. J. 35 (1986) 681-703) for bounded star-shaped domains to the wider class of bounded conformally contractible domains. We give two examples of domains in this class which are not star-shaped. In the case where 1<p<(n+2m)/(n−2m) is subcritical we give lower bounds for the L∞-norm of non-trivial solutions. For certain unbounded conformally contractible domains, 1<p<(n+2m)/(n−2m) subcritical and λ?0 we show that the only smooth solution in H2m−1(Ω) is u≡0. Finally, on a bounded conformally contractible domain uniqueness of non-trivial solutions for f(s)=λ(1+|s|p−1s), p>(n+2m)/(n−2m), supercritical and small λ>0 is proved. Solutions are critical points of a functional on a suitable space X. The theorems are proved by finding one-parameter groups of transformations on X which strictly reduce the values of . Then the uniqueness principle of Part I can be applied. 相似文献
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In an earlier paper the authors showed that with one exception the nonorientable genus of the graph with m≥n−1, the join of a complete graph with a large edgeless graph, is the same as the nonorientable genus of the spanning subgraph . The orientable genus problem for with m≥n−1 seems to be more difficult, but in this paper we find the orientable genus of some of these graphs. In particular, we determine the genus of when n is even and m≥n, the genus of when n=2p+2 for p≥3 and m≥n−1, and the genus of when n=2p+1 for p≥3 and m≥n+1. In all of these cases the genus is the same as the genus of Km,n, namely ⌈(m−2)(n−2)/4⌉. 相似文献