共查询到20条相似文献,搜索用时 15 毫秒
1.
In this work we consider a complete submanifold M with parallel mean curvature vector h immersed in a space form of constant sectional curvature c £ 0c\leq 0. If M has finite total curvature and |H|2 > -c|H|^2>-c, we prove that M must be compact. 相似文献
2.
3.
K. Nakanishi 《Annales Henri Poincare》2002,3(3):503-535
We study modified wave operators for the Hartree equation with a long-range potential |x|-n |x|^{-\nu} , extending the result in [12] to the whole range of the Dollard type 1/2 < n \nu < 1. We construct the modified wave operators in the whole space of (1 + |x|)-sL2 (1 + |x|)^{-s}L^2 . We also have the image, strong continuity and strong asymptotic approximation in the same space. The lower bound $ s > 1 - \nu / 2 $ s > 1 - \nu / 2 of the weight is sharp from the scaling argument. Those maps are homeomorphic onto open subsets, which implies in particular asymptotic completeness for small data. 相似文献
4.
J. Gwoździewicz 《Commentarii Mathematici Helvetici》1999,74(3):364-375
Let f be a real analytic function defined in a neighborhood of
0 ? \Bbb Rn 0 \in {\Bbb R}^n such that f-1(0)={0} f^{-1}(0)=\{0\} . We describe the smallest possible exponents !, #, / for which we have the following estimates: |f(x)| 3 c|x|a |f(x)|\geq c|x|^{\alpha} , |grad f(x)| 3 c|x|b |{\rm grad}\,f(x)|\geq c|x|^{\beta} , |grad f(x)| 3 c|f(x)|q |{\rm grad}\,f(x)|\geq c|f(x)|^{\theta} for x near zero with c > 0 c > 0 . We prove that a = b+1 \alpha=\beta+1, q = b/a\theta=\beta/\alpha . Moreover b = N+a/b \beta=N+a/b where $ 0 h a < b h N^{n-1} $ 0 h a < b h N^{n-1} . If f is a polynomial then |f(x)| 3 c|x|(degf-1)n+1 |f(x)|\geq c|x|^{(\deg f-1)^n+1} in a small neighborhood of zero. 相似文献
5.
We study incompressible Navier–Stokes flows in
\mathbb Rd{\mathbb R^d} with small and well localized data and external force f. We establish pointwise estimates for large |x| of the form ct|x|-d £ |u(x,t)| £ c¢t|x|-d{c_t|x|^{-d}\le |u(x,t)|\le c^\prime_t|x|^{-d}}, where c
t
> 0 whenever ò0tòf(x,s) dx ds 1 0{\int_0^t\int f(x,s)\,dx\,ds\not= {\bf 0}} . This sharply contrasts with the case of the Navier–Stokes equations without force, studied in Brandolese and Vigneron (J
Math Pures Appl 88:64–86, 2007) where the spatial asymptotic behavior was |u(x,t)| @ Ct|x|-d-1{|u(x,t)|\simeq C_t|x|^{-d-1}} . In particular, this shows that external forces with non-zero mean, no matter how small and well localized (say, compactly
supported in space-time), increase the velocity of fluid particles at all times t and at at all points x in the far-field. As an application of our analysis on the pointwise behavior, we deduce sharp upper and lower bounds of
weighted L
p
-norms for strong solutions, extending the results obtained in Bae et al. (to appear) for weak solutions, by considering here
a larger (and in fact, optimal) class of weight functions. 相似文献
6.
Let T be a continuous linear operator on a Banach algebra A. We address the question of whether the constant ${{\rm sup}\{||aT(b)c||: a, b, c \in A, \, ab = bc = 0, ||a|| = ||b|| = ||c||=1\}}Let T be a continuous linear operator on a Banach algebra A. We address the question of whether the constant sup{||aT(b)c||: a, b, c ? A, ab = bc = 0, ||a|| = ||b|| = ||c||=1}{{\rm sup}\{||aT(b)c||: a, b, c \in A, \, ab = bc = 0, ||a|| = ||b|| = ||c||=1\}} being small implies that the distance from T to the space Der(A) of all continuous derivations on A is small. We show that this is the case for amenable group algebras. As a consequence, we deduce that Der(L
1(G)) is hyperreflexive for each amenable group in [SIN]. 相似文献
7.
In the Euclidean Space
\mathbb Rn+1{\mathbb {R}^{n+1}} with a density
ee\frac12 n m2 |x|2, (e = ±1){e^{\varepsilon \frac12 n \mu^2 |x|^2},} {(\varepsilon =\pm1}), we consider the flow of a hypersurface driven by its mean curvature associated to this density. We give a detailed account
of the evolution of a convex hypersurface under this flow. In particular, when e = -1{ \varepsilon=-1} (Gaussian density), the hypersurface can expand to infinity or contract to a convex hypersurface (not necessarily a sphere)
depending on the relation between the bound of its principal curvatures and μ. 相似文献
8.
Piotr Niemiec 《Integral Equations and Operator Theory》2011,71(2):151-160
Generalized absolute values as well as corresponding to them generalized polar decompositions of a bounded linear operator
T of a Hilbert space H{\mathcal{H}} into a Hilbert space K{\mathcal{K}} are defined, motivated by the inequality |áTx, y?K|2 £ á|T|x, x?Há|T*|y, y?K{|\langle{Tx}, {y}\rangle}_{\mathcal{K}}|^2 \leq \langle|T|x, {x}\rangle_{\mathcal{H}}\langle{|T^{*}|y}, {y}\rangle_{\mathcal{K}} . It is shown that there is a natural bijection between generalized absolute values of T and of T* which sends |T| to |T*|. For a bounded nonnegative operator A on H{\mathcal{H}} and a bounded Borel function
f: \mathbbR+ ? \mathbbR+{f: \mathbb{R}_+ \to \mathbb{R}_+} , equivalent conditions for A and f(|T|) to be generalized absolute values of T are established and corresponding to them generalized absolute values of T* are determined. 相似文献
9.
Given an isotropic random vector X with log-concave density in Euclidean space
\mathbbRn{\mathbb{R}^n} , we study the concentration properties of |X| on all scales, both above and below its expectation. We show in particular that
l \mathbbP( | |X| - ?n | 3 t?n ) £ C exp ( -cn1/2 min(t3, t) ) "t 3 0, \begin{array}{l} \mathbb{P}\left ( \left | |X| - \sqrt{n} \right | \geq t\sqrt{n} \right ) \leq C \, {\rm exp} \left ( -cn^{1/2} {\rm min}(t^{3}, t) \right) \; \forall t \geq 0, \end{array} 相似文献
10.
Construction of Wavelet Analysis in the Space of Discrete Splines Using Zak Transform 总被引:4,自引:0,他引:4
Alexander B. Pevnyi Valery A. Zheludev 《Journal of Fourier Analysis and Applications》2002,8(1):59-84
We consider equidistant discrete splines S(j)S(j),
j ? \mathbbZj\in\mathbb{Z}, which may grow as O(|j|s)O(|j|^s) as |j|?¥|j|\to\infty. Such splines present a relevant tool for digital signal processing. The Zak transforms of B-splines yield the integral representation of discrete splines. We define the wavelet space as a weak orthogonal complement of the coarse-grid space in the fine-grid space. We establish the integral representation of the elements of the wavelet space. We define and characterize the wavelets whose shifts form bases of the wavelet space. By this means we design a wide library of bases for the space of discrete-time signals of power growth and construct multiscale representation of this space. We provide formulas for processing such the signals by discrete spline wavelets. Constructed bases are at the same time the Riesz bases for the space l2l_2. 相似文献
11.
Jiabao Su 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,21(2):51-62
We study the existence and multiplicity of nontrivial radial solutions of the quasilinear equation
|