共查询到20条相似文献,搜索用时 281 毫秒
1.
Yu Liu 《Monatshefte für Mathematik》2012,127(2):41-56
Let
Lf(x)=-\frac1w?i,j ?i(ai,j(·)?jf)(x)+V(x)f(x){\mathcal{L}f(x)=-\frac{1}{\omega}\sum_{i,j} \partial_i(a_{i,j}(\cdot)\partial_jf)(x)+V(x)f(x)} with the non-negative potential V belonging to reverse H?lder class with respect to the measure ω(x)dx, where ω(x) satisfies the A
2 condition of Muckenhoupt and a
i,j
(x) is a real symmetric matrix satisfying l-1w(x)|x|2 £ ?ni,j=1ai,j(x)xixj £ lw(x)|x|2.{\lambda^{-1}\omega(x)|\xi|^2\le \sum^n_{i,j=1}a_{i,j}(x)\xi_i\xi_j\le\lambda\omega(x)|\xi|^2. } We obtain some estimates for VaL-a{V^{\alpha}\mathcal{L}^{-\alpha}} on the weighted L
p
spaces and we study the weighted L
p
boundedness of the commutator [b, Va L-a]{[b, V^{\alpha} \mathcal{L}^{-\alpha}]} when b ? BMOw{b\in BMO_\omega} and 0 < α ≤ 1. 相似文献
2.
We construct an explicit intertwining operator L{\mathcal L} between the Schr?dinger group eit \frac\triangle2{e^{it \frac\triangle2}} and the geodesic flow on certain Hilbert spaces of symbols on the cotangent bundle T*X Γ of a compact hyperbolic surface X Γ = Γ\D. We also define Γ-invariant eigendistributions of the geodesic flow PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} (Patterson-Sullivan distributions) out of pairs of \triangle{\triangle} -eigenfunctions, generalizing the diagonal case j = k treated in Anantharaman and Zelditch (Ann. Henri Poincaré 8(2):361–426, 2007). The operator L{\mathcal L} maps PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}} to the Wigner distribution WGj,k{W^{\Gamma}_{j,k}} studied in quantum chaos. We define Hilbert spaces HPS{\mathcal H_{PS}} (whose dual is spanned by {PSj, k, nj,-nk{PS_{j, k, \nu_j,-\nu_k}}}), resp. HW{\mathcal H_W} (whose dual is spanned by {WGj,k}{\{W^{\Gamma}_{j,k}\}}), and show that L{\mathcal L} is a unitary isomorphism from HW ? HPS.{\mathcal H_{W} \to \mathcal H_{PS}.} 相似文献
3.
Andreas W. M. Dress T. Lokot L. D. Pustyl’nikov W. Schubert 《Annals of Combinatorics》2005,8(4):473-485
Given a family of k + 1 real-valued functions
f0 , ?,fkf_0 , \ldots ,f_k defined on the set
{ 1, ?,n}\{ 1, \ldots ,n\} and measuring the intensity of certain signals, we want to investigate whether these functions are T0 , ?,Tk ,T_0 , \ldots ,T_k , the size a of the collection of numbers
j ? { 1, ?,n}j \in \{ 1, \ldots ,n\} whose signals
f0 (j), ?,fk (j)f_0 (j), \ldots ,f_k (j) exceed the corresponding threshold values
T0 , ?,TkT_0 , \ldots ,T_k simultaneously for all
0, ?,k0, \ldots ,k is surprisingly large (or small) in comparison to the family of cardinalities
$
a_i : = \# \{ j \in \{ 1, \ldots ,n\} |f_i (j) > T_i \} \;(i = 0, \ldots ,k)
$
a_i : = \# \{ j \in \{ 1, \ldots ,n\} |f_i (j) > T_i \} \;(i = 0, \ldots ,k)
相似文献
4.
We investigate properties of entire solutions of differential equations of the form
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