2015年2期 (共 篇) 引用文章 全选
A Marcinkiewicz criterion for Lp-multipliers related to Schrödinger operators with constant magnetic fields
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In this paper, we follow Dappa's work to establish the Marcinkiewicz criterion for the spectral multipliers related to the Schrödinger operator with a constant magnetic field. We prove that if m and m' are locally absolutely continuous on (0,∞) and
then the multiplier defined by m(t) is bounded on Lp for 2n/(n+3) < p < 2n/(n-3) with n ≥ 3. Our approach is based on the estimates for the generalized Littlewood-Paley functions of the spectral representation of the Schrödinger operator with a constant magnetic field.
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In the case where either the potentials Vj, μj and β are periodic or Vj are well-shaped and μj and β are anti-well-shaped, existence of a positive ground state of the Schrödinger system
where N = 1, 2, 3, is proved provided that β is either small or large in terms of Vj and μj . The system with constant coefficients has been studied extensively in the last ten years, and the nonconstant coefficients case has seldom been studied. It turns out that new technical machineries in the setting of variational methods are needed in dealing with the nonconstant coefficients case.
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We introduce the notion of weak k-hyponormality and polynomial hyponormality for commuting operator pairs on a Hilbert space and investigate their relationship with k-hyponormality and subnormality. We provide examples of 2-variable weighted shifts which are weakly 1-hyponormal but not hyponormal. By relating the weak k-hyponormality and k-hyponormality of a commuting operator pair to positivity of restriction of some linear functionals to corresponding cones of functions, we prove that there is an operator pair that is polynomially hyponormal but not 2-hyponormal, generalizing Curto and Putinar's result (1991, 1993) to the two-variable case.
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In this paper, we extend Su-Zhang's Cheeger-Müller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary. Our result also extends Brüning-Ma's Cheeger-Müller type theorem for Ray-Singer metric on manifolds with boundary to symmetric bilinear torsions in product case. We also compare it with the Ray-Singer analytic torsion on manifolds with boundary.
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An additive functor F: A → B between additive categories is said to be objective, provided any morphism f in A with F(f) = 0 factors through an object K with F(K) = 0. We concentrate on triangle functors between triangulated categories. The first aim of this paper is to characterize objective triangle functors F in several ways. Second, we are interested in the corresponding Verdier quotient functors VF: A → A/KerF, in particular we want to know under what conditions VF is full. The third question to be considered concerns the possibility to factorize a given triangle functor F = F2F1 with F1 a full and dense triangle functor and F2 a faithful triangle functor. It turns out that the behavior of splitting monomorphisms and splitting epimorphisms plays a decisive role.
本平台内已出版文章查询 , CHANG XiangKe 已出版文章查询
本平台内已出版文章查询 , HU Juan 已出版文章查询
本平台内已出版文章查询 , HU XingBiao 已出版文章查询
本平台内已出版文章查询 , TAM Hon-Wah 已出版文章查询
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We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota's bilinear method. This approach is mainly based on the compatibility between an integrable system and its Bäcklund transformation. We apply this procedure to several equations, including the extended Korteweg-de- Vries (KdV) equation, the extended Kadomtsev-Petviashvili (KP) equation, the extended Boussinesq equation, the extended Sawada-Kotera (SK) equation and the extended Ito equation, and obtain their associated semidiscrete analogues. In the continuum limit, these differential-difference systems converge to their corresponding smooth equations. For these new integrable systems, their Bäcklund transformations and Lax pairs are derived.
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It is well known by the strong multiplicity one that π is uniquely determined by the Satake parameter c(π, v) for almost all v. Also, it suffices for us to test only finitely many v. We proved some S-effective version of multiplicity one theorems. Roughly speaking, if π and π' are not equivalent, then there is also a bound N(S) which is some expression in terms of K, d and max(N(π),N(π')), which are analytic conductor of π and π', respectively (will be defined soon), such that there is a v/S with πvπv' and Npv < N. We also proved S-effective multiplicity one for the Chebotarev Density Theorem, and for GL(1).
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A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed, where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1 polynomial vectors, for all k ≥ 4. The main ingredients for the analysis are a new basis of the space of symmetric matrices, an intrinsic H(div) bubble function space on each element, and a new technique for establishing the discrete inf-sup condition. In particular, they enable us to prove that the divergence space of the H(div) bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1 polynomial space on each tetrahedron. The optimal error estimate is proved, verified by numerical examples.
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Let (X, d, μ) be a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. Let ρ ∈ (1,∞), 0 < p ≤ 1 ≤ q ≤ ∞, p ≠ q, γ ∈ [1,∞) and ε ∈ (0,∞). In this paper, the authors introduce the atomic Hardy space (μ) and the molecular Hardy space (μ) via the discrete coefficient , and prove that the Calderón-Zygmund operator is bounded from (μ) (or (μ)) into Lp(μ), and from (μ) into (μ). The boundedness of the generalized fractional integral Tβ (β ∈ (0, 1)) from (μ) (or (μ)) into Lp2(μ) with 1/p2 = 1/p1-β is also established. The authors also introduce the ρ-weakly doubling condition, with ρ ∈ (1,∞), of the measure μ and construct a non-doubling measure μ satisfying this condition. If μ is ρ-weakly doubling, the authors further introduce the Campanato space (μ) and show that (μ) is independent of the choices of ρ, η, γ and q; the authors then introduce the atomic Hardy space (μ) and the molecular Hardy space (μ), which coincide with each other; the authors finally prove that ??? (μ) is the predual of (μ). Moreover, if μ is doubling, the authors show that (μ) and the Lipschitz space Lipα,q(μ) (q ∈ [1,∞)), or (μ) and the atomic Hardy space Hatp,q(μ) (q ∈ (1,∞]) of Coifman and Weiss coincide. Finally, if (X, d, μ) is an RD-space (reverse doubling space) with μ(X) = ∞, the authors prove that (μ), (μ) and Hatp,q(μ) coincide for any q ∈ (1, 2]. In particular, when (X, d, μ):= (RD, |·|, dx) with dx being the D-dimensional Lebesgue measure, the authors show that spaces (μ), (μ), (μ) and ???(μ) all coincide with Hp(RD) for any q ∈ (1,∞).
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Let L be a Lévy process with characteristic measure v, which has an absolutely continuous lower bound w.r.t. the Lebesgue measure on Rn. By using Malliavin calculus for jump processes, we investigate Bismut formula, gradient estimates and coupling property for the semigroups associated to semilinear SDEs forced by Lévy process L.