共查询到10条相似文献,搜索用时 545 毫秒
1.
Oversampling generates super-wavelets 总被引:1,自引:0,他引:1
Dorin Ervin Dutkay Palle Jorgensen 《Proceedings of the American Mathematical Society》2007,135(7):2219-2227
We show that the second oversampling theorem for affine systems generates super-wavelets. These are frames generated by an affine structure on the space .
2.
Local Dispersive and Strichartz Estimates for the Schrödinger Operator on the Heisenberg Group
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Hajer Bahouri & Isabelle Gallagher 《数学研究通讯:英文版》2023,39(1):1-35
It was proved by Bahouri et al. [9] that the Schrödinger equation on
the Heisenberg group $\mathbb{H}^d,$ involving the sublaplacian, is an example of a totally
non-dispersive evolution equation: for this reason global dispersive estimates
cannot hold. This paper aims at establishing local dispersive estimates on $\mathbb{H}^d$ for the linear Schrödinger equation, by a refined study of the Schrödinger kernel $S_t$ on $\mathbb{H}^d.$ The sharpness of these estimates is discussed through several
examples. Our approach, based on the explicit formula of the heat kernel on $\mathbb{H}^d$ derived by Gaveau [19], is achieved by combining complex analysis and
Fourier-Heisenberg tools. As a by-product of our results we establish local Strichartz estimates and prove that the kernel $S_t$ concentrates on quantized horizontal hyperplanes of $\mathbb{H}^d.$ 相似文献
3.
Adam Osȩkowski 《Complex Analysis and Operator Theory》2014,8(6):1269-1283
The paper is devoted to the \(d\) -dimensional extension of the classical identity of Stein and Weiss concerning the action of the Hilbert transform on characteristic functions. Let \((R_j)_{j=1}^d\) be the collection of Riesz transforms in \(\mathbb{R }^d\) . For \(1\le p<\infty \) , we determine the least constants \(c_{p,d}, C_{p,d}\) such that $$\begin{aligned} \int _{\mathbb{R }^d} f(x)|R_jf(x)|^p\text{ d }x&\le c_{p,d} ||f||_{L^1(\mathbb{R }^d)},\\ \int _{\mathbb{R }^d} (1-f(x))|R_jf(x)|^p\text{ d }x&\le C_{p,d} ||f||_{L^1(\mathbb{R }^d)} \end{aligned}$$ for any Borel function \(f:\mathbb{R }^d\rightarrow [0,1]\) . The proof rests on probabilistic methods and the construction of appropriate harmonic functions on \([0,1]\times \mathbb{R }\) . 相似文献
4.
JIANG Yanjie 《中国科学A辑(英文版)》2000,43(6):609-615
This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes Srp q θb(Rd) and Srp q θB(Rd) in Lq(Rd) (1≤q≤p<∞). The weak asymptotic behavior is established for the corresponding quantities. 相似文献
5.
In this note we investigate the asymptotic behavior of the solutions of the heat equation with random, fast oscillating potential
${rcl} \partial_tu_{\varepsilon}(t,x)&=&\dfrac12\Delta_xu_{\varepsilon}(t,x)+{\varepsilon}^{-\gamma}V\left(\dfrac{x}{{\varepsilon}}\right)u_{\varepsilon}(t,x),\,(t,x)\in(0,+\infty)\times{\mathbb R}^d, \\ u_{\varepsilon}(0,x)&=&u_0(x),\,x\in{\mathbb R}^d, $\begin{array}{rcl} \partial_tu_{\varepsilon}(t,x)&=&\dfrac12\Delta_xu_{\varepsilon}(t,x)+{\varepsilon}^{-\gamma}V\left(\dfrac{x}{{\varepsilon}}\right)u_{\varepsilon}(t,x),\,(t,x)\in(0,+\infty)\times{\mathbb R}^d, \\ u_{\varepsilon}(0,x)&=&u_0(x),\,x\in{\mathbb R}^d, \end{array} 相似文献
6.
L. I. Ignat D. Pinasco J. D. Rossi A. San Antolin 《Journal d'Analyse Mathématique》2014,122(1):375-401
In this paper, we obtain bounds for the decay rate in the L r (? d )-norm for the solutions of a nonlocal and nonlinear evolution equation, namely, $$u_t \left( {x,t} \right) = \int_{\mathbb{R}^d } {K\left( {x,y} \right)\left| {u\left( {y,t} \right) - u\left( {x,t} \right)} \right|^{p - 2} \left( {u\left( {y,t} \right) - u\left( {x,t} \right)} \right)dy, x \in \mathbb{R}^d , t > 0.}$$ . We consider a kernel of the form K(x, y) = ψ(y?a(x)) + ψ(x?a(y)), where ψ is a bounded, nonnegative function supported in the unit ball and a is a linear function a(x) = Ax. To obtain the decay rates, we derive lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form $$T\left( u \right) = - \int_{\mathbb{R}^d } {K\left( {x,y} \right)\left| {u\left( y \right) - u\left( x \right)} \right|^{p - 2} \left( {u\left( y \right) - u\left( x \right)} \right)dy, 1 \leqslant p < \infty .}$$ . The upper and lower bounds that we obtain are sharp and provide an explicit expression for the first eigenvalue in the whole space ? d : $$\lambda _{1,p} \left( {\mathbb{R}^d } \right) = 2\left( {\int_{\mathbb{R}^d } {\psi \left( z \right)dz} } \right)\left| {\frac{1} {{\left| {\det A} \right|^{1/p} }} - 1} \right|^p .$$ Moreover, we deal with the p = ∞ eigenvalue problem, studying the limit of λ 1,p 1/p as p→∞. 相似文献
7.
设$f_n$是基于核函数$K$和取值于$d$-维单位球面${\mathbb{S}}^{d-1}$的独立同分布随机变量列的非参数核密度估计. 我们证明了若核函数是有界变差函数, 随机变量的密度函数$f$是连续的和对称的, $\{\sup_{x\in {\mathbb{SS}}^{d-1}}|f_n(x)-f_n(-x)|,n\ge 1\}$的大偏差原理成立. 相似文献
8.
9.
Ferenc Weisz 《Monatshefte für Mathematik》2014,175(1):143-160
New multi-dimensional Wiener amalgam spaces \(W_c(L_p,\ell _\infty )(\mathbb{R }^d)\) are introduced by taking the usual one-dimensional spaces coordinatewise in each dimension. The strong Hardy-Littlewood maximal function is investigated on these spaces. The pointwise convergence in Pringsheim’s sense of the \(\theta \) -summability of multi-dimensional Fourier transforms is studied. It is proved that if the Fourier transform of \(\theta \) is in a suitable Herz space, then the \(\theta \) -means \(\sigma _T^\theta f\) converge to \(f\) a.e. for all \(f\in W_c(L_1(\log L)^{d-1},\ell _\infty )(\mathbb{R }^d)\) . Note that \(W_c(L_1(\log L)^{d-1},\ell _\infty )(\mathbb{R }^d) \supset W_c(L_r,\ell _\infty )(\mathbb{R }^d) \supset L_r(\mathbb{R }^d)\) and \(W_c(L_1(\log L)^{d-1},\ell _\infty )(\mathbb{R }^d) \supset L_1(\log L)^{d-1}(\mathbb{R }^d)\) , where \(1
10.
We develop conditions on a Sobolev function \(\psi \in W^{m,p}({\mathbb{R}}^d)\) such that if \(\widehat{\psi}(0) = 1\) and ψ satisfies the Strang–Fix conditions to order m ? 1, then a scale averaged approximation formula holds for all \(f \in W^{m,p}({\mathbb{R}}^d)\) : 相似文献
$ f(x) = \lim_{J \to \infty} \frac{1}{J} \sum_{j=1}^{J} \sum_{k \in {{\mathbb{Z}}}^d} c_{j,k}\psi(a_j x - k) \quad {\rm in} W^{m, p}({{\mathbb{R}}}^d).$ |