共查询到20条相似文献,搜索用时 46 毫秒
1.
Jun Wu 《Monatshefte für Mathematik》2006,149(3):259-264
For
, let E(λ*, λ*) be the set
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
where dim denotes the Hausdorff dimension. 相似文献
2.
H. Rindler 《Monatshefte für Mathematik》2006,147(3):265-272
For
, let E(λ*, λ*) be the set
It has been proved in [1] and [3] that E(λ*, λ*) is an uncountable set. In the present paper, we strengthen this result by showing that
where dim denotes the Hausdorff dimension. 相似文献
3.
We consider the spectral decomposition of A, the generator of a polynomially bounded n-times integrated group whose spectrum set $\sigma(A)=\{i\lambda_{k};k\in\mathbb{\mathbb{Z}}^{*}\}We consider the spectral decomposition of A, the generator of a polynomially bounded n-times integrated group whose spectrum set
s(A)={ilk;k ? \mathbb\mathbbZ*}\sigma(A)=\{i\lambda_{k};k\in\mathbb{\mathbb{Z}}^{*}\}
is discrete and satisfies
?\frac1|lk|ldkn < ¥\sum \frac{1}{|\lambda_{k}|^{\ell}\delta_{k}^{n}}<\infty
, where ℓ is a nonnegative integer and
dk=min(\frac|lk+1-lk|2,\frac|lk-1-lk|2)\delta _{k}=\min(\frac{|\lambda_{k+1}-\lambda _{k}|}{2},\frac{|\lambda _{k-1}-\lambda _{k}|}{2})
. In this case, Theorem 3, we show by using Gelfand’s Theorem that there exists a family of projectors
(Pk)k ? \mathbb\mathbbZ*(P_{k})_{k\in\mathbb{\mathbb{Z}}^{*}}
such that, for any x∈D(A
n+ℓ
), the decomposition ∑P
k
x=x holds. 相似文献
4.
N. A. Veniaminov 《Journal of Mathematical Sciences》2010,169(1):46-63
We study the asymptotics of the spectrum of the Maxwell operator M in a bounded Lipschitz domain
W ì \mathbbR3 \Omega \subset {\mathbb{R}^3} under the condition of the perfect conductivity of the boundary ∂Ω. We obtain the following estimate for the remainder in
the Weyl asymptotic expansion of the counting function N(λ,M) of positive eigenvalues of the Maxwell operator M:
N( l, M ) = \frac\textmeas W3p2l3( 1 + O( l - 2 | / |
5 ) ), N\left( {\lambda, M} \right) = \frac{{{\text{meas }}\Omega }}{{3{\pi^2}}}{\lambda^3}\left( {1 + O\left( {{\lambda^{{{{ - 2}} \left/ {5} \right.}}}} \right)} \right), 相似文献
5.
Nam Q. Le 《Geometriae Dedicata》2011,151(1):361-371
Consider a family of smooth immersions
F(·,t) : Mn? \mathbbRn+1{F(\cdot,t)\,:\,{M^n\to \mathbb{R}^{n+1}}} of closed hypersurfaces in
\mathbbRn+1{\mathbb{R}^{n+1}} moving by the mean curvature flow
\frac?F(p,t)?t = -H(p,t)·n(p,t){\frac{\partial F(p,t)}{\partial t} = -H(p,t)\cdot \nu(p,t)}, for t ? [0,T){t\in [0,T)}. We show that at the first singular time of the mean curvature flow, certain subcritical quantities concerning the second
fundamental form, for example
ò0tòMs\frac|A|n + 2 log (2 + |A|) dmds,{\int_{0}^{t}\int_{M_{s}}\frac{{\vert{\it A}\vert}^{n + 2}}{ log (2 + {\vert{\it A}\vert})}} d\mu ds, blow up. Our result is a log improvement of recent results of Le-Sesum, Xu-Ye-Zhao where the scaling invariant quantities
were considered. 相似文献
6.
Suppose f∈Hp(Tn), 0 r δ , δ=n/p?(n+1)/2. In this paper we eastablish the following inequality $$\mathop {\sup }\limits_{R > 1} \left\{ {\frac{1}{{\log R}}\int_1^R {\left\| {\sigma _r^\delta } \right\|_{H^p (T^R )}^p \frac{{dr}}{r}} } \right\}^{1/p} \leqslant C_{R,p} \left\| f \right\|_{H^p (T^R )} $$ It implies that $$\mathop {\lim }\limits_{R \to \infty } \frac{1}{{\log R}}\int_1^R {\left\| {\sigma _r^\delta - f} \right\|_{H^p (T^R )}^p \frac{{dr}}{r}} = 0$$ Moreover we obtain the same conclusion when p=1 and n=1. 相似文献
7.
In this paper, we consider massless Dirac fields propagating in the outer region of de Sitter–Reissner–Nordstr?m black holes.
We show that the metric of such black holes is uniquely determined by the partial knowledge of the corresponding scattering
matrix S(λ) at a fixed energy λ ≠ 0. More precisely, we consider the partial wave scattering matrices S(λ, n) (here λ ≠ 0 is the fixed energy and
n ? \mathbbN*{n \in \mathbb{N}^{*}} denotes the angular momentum) defined as the restrictions of the full scattering matrix on a well chosen basis of spin-weighted
spherical harmonics. We prove that the mass M, the square of the charge Q
2 and the cosmological constant Λ of a dS-RN black hole (and thus its metric) can be uniquely determined from the knowledge
of either the transmission coefficients T(λ, n), or the reflexion coefficients R(λ, n) (resp. L(λ, n)), for all n ? L{n \in {\mathcal{L}}} where L{\mathcal{L}} is a subset of
\mathbbN*{\mathbb{N}^{*}} that satisfies the Müntz condition
?n ? L\frac1n = +¥{\sum_{n \in{\mathcal{L}}}\frac{1}{n} = +\infty} . Our main tool consists in complexifying the angular momentum n and in studying the analytic properties of the “unphysical” scattering matrix S(λ, z) in the complex variable z. We show, in particular, that the quantities
\frac1T(l,z){\frac{1}{T(\lambda,z)}},
\fracR(l,z)T(l,z){\frac{R(\lambda,z)}{T(\lambda,z)}} and
\fracL(l,z)T(l,z){\frac{L(\lambda,z)}{T(\lambda,z)}} belong to the Nevanlinna class in the region ${\{z \in \mathbb{C}, Re(z) > 0 \}}${\{z \in \mathbb{C}, Re(z) > 0 \}} for which we have analytic uniqueness theorems at our disposal. Eventually, as a by-product of our method, we obtain reconstruction
formulae for the surface gravities of the event and cosmological horizons of the black hole which have an important physical
meaning in the Hawking effect. 相似文献
8.
LetR
n be n-dimensional Euclidean space with n>-3. Demote by Ω
n
the unit sphere inR
n. ForfɛL(Ω
n
) we denote by σ
N
δ
its Cesàro means of order σ for spherical harmonic expansions. The special value
l = \tfracn - 22\lambda = \tfrac{{n - 2}}{2}
of σ is known as the critical one. For 0<σ≤λ, we set
p0 = \tfrac2ld+ lp_0 = \tfrac{{2\lambda }}{{\delta + \lambda }}
.
This paper proves that
|