共查询到20条相似文献,搜索用时 15 毫秒
1.
It was conjectured by the first author and Peetre that the higher Laplace–Beltrami operators generate the whole ring of invariant operators on bounded symmetric domains. We give a proof of the conjecture for domains of rank ≤ 6 by using a graph manipulation of K¨ahler curvature tensor. We also compute higher order terms in the asymptotic expansions of the Bergman kernels and the Berezin transform on bounded symmetric domain. 相似文献
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Mathematical Notes - 相似文献
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Let \(\Delta _0\) be the Laplace–Beltrami operator on the unit sphere \(\mathbb {S}^{d-1}\) of \({\mathbb R}^d\) . We show that the Hardy–Rellich inequality of the form $$\begin{aligned} \mathop \int \limits _{\mathbb {S}^{d-1}} \left| f (x)\right| ^2 \mathrm{d}{\sigma }(x) \le c_d \min _{e\in \mathbb {S}^{d-1}} \mathop \int \limits _{\mathbb {S}^{d-1}} (1- {\langle }x, e {\rangle }) \left| (-\Delta _0)^{\frac{1}{2}}f(x) \right| ^2 \mathrm{d}{\sigma }(x) \end{aligned}$$ holds for \(d =2\) and \(d \ge 4\) but does not hold for \(d=3\) with any finite constant, and the optimal constant for the inequality is \(c_d = 8/(d-3)^2\) for \(d =2, 4, 5,\) and, under additional restrictions on the function space, for \(d\ge 6\) . This inequality yields an uncertainty principle of the form $$\begin{aligned} \min _{e\in \mathbb {S}^{d-1}} \mathop \int \limits _{\mathbb {S}^{d-1}} (1- {\langle }x, e {\rangle }) |f(x)|^2 \mathrm{d}{\sigma }(x) \mathop \int \limits _{\mathbb {S}^{d-1}}\left| \nabla _0 f(x)\right| ^2 \mathrm{d}{\sigma }(x) \ge c'_d \end{aligned}$$ on the sphere for functions with zero mean and unit norm, which can be used to establish another uncertainty principle without zero mean assumption, both of which appear to be new. 相似文献
4.
Differential Equations - The first and second initial–boundary value problems are considered for a second-order Petrovskii parabolic system with variable coefficients in a bounded domain with... 相似文献
5.
The inhomogeneous Robin condition with general coefficient for the overdetermined inhomogeneous Cauchy–Riemann system of equations
on the polydisc is studied using Fourier analysis. It is shown that this problem for the case of nonholomorphic general coefficient,
is actually a problem with essential singularity in the domain, but still well-posed under certain compatibility conditions.
Under proper assumptions, the unique solution is given explicitly. 相似文献
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Differential Equations - We consider the Cauchy problem for the Emden–Fowler equation $$y^{prime {}prime }-x^ay^{sigma }=0 $$ with parameters $$ain mathbb {R} $$ and $$sigma <0... 相似文献
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By reflections, we obtain the Schwarz?CPoisson formula in a sector with angle ${\vartheta=\frac{\pi}{n},\,n\in \mathbb{N}}$ , which is a generalization of the corresponding result obtained by Begehr and Vaitekhovich (Funct Approx 40(2):251?C282, 2009). Especially, boundary behaviors at corner points are discussed in detail. Then we consider the Schwarz and Dirichlet boundary-value problems (BVPs) for the Cauchy?CRiemann equation, and expressions of solution and the condition of solvability are explicitly obtained. 相似文献
9.
Fethi Soltani 《Complex Analysis and Operator Theory》2014,8(1):311-325
We give an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev spaces associated with a singular second-order differential operator. Next, we come up with some results regarding the multiplier operators for the Sturm–Liouville transform. 相似文献
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The purpose of this Note is to extend to any space dimension the bilinear estimate for eigenfunctions of the Laplace operator on a compact manifold (without boundary) obtained by the authors (preprint: http://www.arxiv.org/abs/math/0308214) in dimension 2. We also give some related trilinear estimates. To cite this article: N. Burq et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
12.
Gao Mingchu 《东北数学》1998,(1)
in this paper, we first give a Hille-Yosida type sufficient and necessary conditionfor n-times integrated mild C-existence families. Then, we present a Laplace type sufficientand necessary condition for exponentially bounded n-times integrated C-semigrougs, andstudy the relationship between integrated regularized semigroups and general regularizedsemigroups. Finally, we offer a characterization of integrated C-semigroups in terms of thesolvability of abstract Cauchy problems. 相似文献
13.
Yu Xiang LI 《数学学报(英文版)》2006,22(2):545-550
We will show in this paper that if A is very close to 1, then
I(M,λ,m) =supu∈H0^1,n(m),∫m|△↓u|^ndV=1∫Ω(e^αn|u|^n/(n-1)-λm∑k=1|αnun/(n-1)|k/k!)dV
can be attained, where M is a compact-manifold with boundary. This result gives a counter-example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" (Comm. Pure. Appl. Math., 55, 135-152, 2002). 相似文献
14.
W. Ramasinghe 《International Journal of Mathematical Education in Science & Technology》2013,44(1):35-41
It is very well known that the Cauchy–Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy–Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real vector space with a product satisfying properties of an inner product except the homogeneous property induces a metric but not a norm. It is remarkable to see that the metric induced on the real line by such a product has highly contrasting properties relative to the absolute value metric. In particular, such a product on the real line is given so that the induced metric is not complete and the set of rational numbers is not dense in the real line. 相似文献
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Cheng-Shi Liu 《Applied Mathematics Letters》2013,26(9):957-962
By a simple mathematical method, we obtain the transition probability density functions of the Ornstein–Uhlenbeck process, Cauchy process, and Ornstein–Uhlenbeck–Cauchy process on a circle. 相似文献
17.
Géza Tóth 《Discrete and Computational Geometry》2008,39(4):791-799
The crossing number
of a graph G is the minimum possible number of edge-crossings in a drawing of G, the pair-crossing number
is the minimum possible number of crossing pairs of edges in a drawing of G, and the odd-crossing number
is the minimum number of pairs of edges that cross an odd number of times. Clearly,
. We construct graphs with
. This improves the bound of Pelsmajer, Schaefer and Štefankovič. Our construction also answers an old question of Tutte.
Slightly improving the bound of Valtr, we also show that if the pair-crossing number of G is k, then its crossing number is at most O(k
2/log 2
k).
G. Tóth’s research was supported by the Hungarian Research Fund grant OTKA-K-60427 and the Research Foundation of the City
University of New York. 相似文献
18.
Manfred Reimer 《Results in Mathematics》1999,36(3-4):331-341
Applying a quadrature rule with positive weights to some integral operators introduced by Newman and Shapiro we obtain generalized hyperinterpolation operators on the sphere, whose approximation error can be estimated — inspite of the discretisation — by means of the modulus of continuity. The main reason is that the weight distribution satisfies necessarily some regularity condition, which has been used before in hyperinterpolation by Sloan and Womersley, and which turned out to hold always by its own. 相似文献
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Considering the Teichmüller space of a surface equipped with Thurston’s Lipschitz metric, we study geodesic segments whose endpoints have bounded combinatorics. We show that these geodesics are cobounded, and that the closest-point projection to these geodesics is strongly contracting. Consequently, these geodesics are stable. Our main tool is to show that one can get a good estimate for the Lipschitz distance by considering the length ratio of finitely many curves. 相似文献