共查询到20条相似文献,搜索用时 839 毫秒
1.
We consider two-phase metrics of the form ϕ(x, ξ) ≔
, where α,β are fixed positive constants and B
α, B
β are disjoint Borel sets whose union is ℝN, and prove that they are dense in the class of symmetric Finsler metrics ϕ satisfying
. Then we study the closure
of the class
of two-phase periodic metrics with prescribed volume fraction θ of the phase α. We give upper and lower bounds for the class
and localize the problem, generalizing the bounds to the non-periodic setting. Finally, we apply our results to study the
closure, in terms of Γ-convergence, of two-phase gradient-constraints in composites of the type f(x, ∇ u) ≤ C(x), with C(x) ∈ {α, β } for almost every x. 相似文献
2.
Luca Brandolini Alex Iosevich Giancarlo Travaglini 《Journal of Fourier Analysis and Applications》2001,7(4):359-372
Let Γ be a smooth compact convex planar curve with arc length dm and let dσ=ψ dm where ψ is a cutoff function. For Θ∈SO (2)
set σΘ(E) = σ(ΘE) for any measurable planar set E. Then, for suitable functions f in ℝ2, the inequality.
represents an average over rotations, of the Stein-Tomas restriction phenomenon. We obtain best possible indices for the
above inequality when Γ is any convex curve and under various geometric assumptions. 相似文献
3.
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 .
4.
L. G. Arabadzhyan 《Mathematical Notes》1997,62(3):271-277
We study the solvability of the integral equation
, wheref∈L
1
loc(ℝ) is the unknown function andg,T
1, andT
2 are given functions satisfying the conditions
.
Most attention is paid to the nontrivial solvability of the homogeneous equation
.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 323–331, September, 1997.
Translated by M. A. Shishkova 相似文献
5.
Liu Yongping 《分析论及其应用》1992,8(4):79-88
In this paper, a kind of generalized Sobolev-Wiener classes
, h>0, defined on the whole real axis, is introduced, and the average σ-K width problem of these function classes in the metric
is studied. For the case p=+∞, 1≤q≤+∞, the case 1≤p <+∞, q=1, we get their exact values and identify their optimal subspaces.
This project supported by YNSFC 相似文献
6.
GuiQiaoXU YongPingLIU 《数学学报(英文版)》2004,20(1):81-92
This paper concerns the problem of average σ-width of Sobolev-Wiener classes W^rpq(R^d),W^rpq(M,R^d),and Besov-Wiener classes S^rpqθb(R^d).S^rpqθB(R^d),S^rpqθb(M,R^d),S^rpqθB(R^d)in the metric Lq(R^d) for 1≤q≤p≤∞.The weak asymptotic results concerning the average linear widths,the average Bernstein widths and the infinite-dimensional Gel‘fand widths are obtained,respectively. 相似文献
7.
Zhang Lixin 《数学学报(英文版)》1998,14(1):113-124
Let {X, X
n
;n>-1} be a sequence of i.i.d.r.v.s withEX=0 andEX
2=σ2(0 < σ < ∞).
we obtain some sufficient and necessary conditions for
to hold, get the widest range ofk’s and answer a question of Hanson and Russo (1983).
Supported by National Natural Science Foundation of China and China Postdoctoral Science Foundation 相似文献
8.
T. Kühn 《Proceedings of the Steklov Institute of Mathematics》2006,255(1):159-168
The exact asymptotic behavior of the entropy numbers of compact embeddings of weighted Besov spaces is known in many cases,
in particular for power-type weights and logarithmic weights. Here we consider intermediate weights that are strictly between
these two scales; a typical example is
. For such weights we prove almost optimal estimates of the entropy numbers e
k
(id:
).
Dedicated to Sergeĭ Mikhaĭlovich Nikol’skiĭ on the occasion of his 100th birthday 相似文献
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 . Moreover, \(\sigma _T^\theta f(x)\) converges to \(f(x)\) at each Lebesgue point of \(f\in W_c(L_1(\log L)^{d-1},\ell _\infty )(\mathbb{R }^d)\) . 相似文献
10.
Qingfeng Sun 《Central European Journal of Mathematics》2011,9(2):328-337
Let λ(n) be the Liouville function. We find a nontrivial upper bound for the sum
$
\sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R}
$
\sum\limits_{X \leqslant n \leqslant 2X} {\lambda (n)e^{2\pi i\alpha \sqrt n } } ,0 \ne \alpha \in \mathbb{R}
相似文献
11.
Necessary and sufficient conditions are derived in order that an inequality of the form
|