共查询到20条相似文献,搜索用时 46 毫秒
1.
Jun Wu 《Monatshefte für Mathematik》2006,54(4):259-264
For
log\frac1+?52 £ l* £ l* < ¥{\rm log}\frac{1+\sqrt{5}}{2}\leq \lambda_\ast \leq \lambda^\ast < \infty
, let E(λ*, λ*) be the set
{x ? [0,1): liminfn ? ¥\fraclogqn(x)n=l*, limsupn ? ¥\fraclogqn(x)n=l*}. \left\{x\in [0,1):\ \mathop{\lim\inf}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda_{\ast}, \mathop{\lim\sup}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda^{\ast}\right\}.
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
dimE(l*, l*) 3 \fracl* -log\frac1+?522l*\dim E(\lambda_{\ast}, \lambda^{\ast}) \ge \frac{\lambda_{\ast} -\log \frac{1+\sqrt{5}}{2}}{2\lambda^{\ast}} 相似文献
2.
Flávio Dickstein Miguel Loayza 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,24(10):1-23
We consider the Cauchy problem for the weakly coupled parabolic system ∂
t
w
λ−Δ w
λ = F(w
λ) in R
N
, where λ > 0, w
λ = (u
λ, v
λ), F(w
λ) = (v
λ
p
, u
λ
q
) for some p, q ≥ 1, pq > 1, and
wl(0) = (lj1, l\fracq+1p+1j2)w_{\lambda}(0) = ({\lambda}{\varphi}_1, {\lambda}^{\frac{q+1}{p+1}}{\varphi}_2), for some nonnegative functions φ1, φ2
?\in
C
0(R
N
). If (p, q) is sub-critical or either φ1 or φ2 has slow decay at ∞, w
λ blows up for all λ > 0. Under these conditions, we study the blowup of w
λ for λ small. 相似文献
3.
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
4.
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
5.
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
6.
Yong Fang 《Geometriae Dedicata》2010,145(1):139-150
Let g be a negatively curved Riemannian metric of a closed C
∞ manifold M of dimension at least three. Let L
λ be a C
∞ one-parameter convex superlinear Lagrangian on TM such that
L0(v) = \frac12 g(v, v){L_0(v)= \frac{1}{2} g(v, v)} for any v ∈ TM. We denote by jl{\varphi^\lambda} the restriction of the Euler-Lagrange flow of L
λ on the
\frac12{\frac{1}{2}} -energy level. If λ is small enough then the flow jl{\varphi^\lambda} is Anosov. In this paper we study the geometric consequences of different assumptions about the regularity of the Anosov
distributions of jl{\varphi^\lambda} . For example, in the case that the initial Riemannian metric g is real hyperbolic, we prove that for λ small, jl{\varphi^\lambda} has C
3 weak stable and weak unstable distributions if and only if jl{\varphi^\lambda} is C
∞ orbit equivalent to the geodesic flow of g. 相似文献
7.
Djordje Mili?evi? 《Geometric And Functional Analysis》2011,21(6):1375-1418
We prove that, on a distinguished class of arithmetic hyperbolic 3-manifolds, there is a sequence of L
2-normalized high-energy Hecke–Maass eigenforms fj{\phi_{j}} which achieve values as large as l1/4+o(1)j{\lambda^{1/4+o(1)}_{j}}, where ( D+lj ) fj = 0{( \Delta+\lambda_{j} ) \phi_{j} = 0}. Arithmetic hyperbolic 3-manifolds on which this exceptional behavior is exhibited are, up to commensurability, precisely
those containing immersed totally geodesic surfaces. We adapt the method of resonators and connect values of eigenfunctions
to the global geometry of the manifold by employing the pre-trace formula and twists by Hecke correspondences. Automorphic
representations corresponding to forms appearing with highest weights in the optimized spectral averages are characterized
both in terms of base change lifts and in terms of theta lifts from GSp2. 相似文献
8.
Wolfgang Müller 《Monatshefte für Mathematik》2011,171(2):69-88
Denote by 0 = λ
0 < λ
1 ≤ λ
2 ≤ . . . the infinite sequence given by the values of a positive definite irrational quadratic form in k variables at integer points. For l ≥ 2 and an (l −1)-dimensional interval I = I
2×. . .×I
l
we consider the l-level correlation function K(l)I(R){K^{(l)}_I(R)} which counts the number of tuples (i
1, . . . , i
l
) such that li1,?,lil £ R2{\lambda_{i_1},\ldots,\lambda_{i_l}\leq R^2} and lij-li1 ? Ij{\lambda_{i_{j}}-\lambda_{i_{1}}\in I_j} for 2 ≤ j ≤ l. We study the asymptotic behavior of K(l)I(R){K^{(l)}_I(R)} as R tends to infinity. If k ≥ 4 we prove K(l)I(R) ~ cl(Q) vol(I)Rlk-2(l-1){K^{(l)}_I(R)\sim c_l(Q)\,{\rm vol}(I)R^{lk-2(l-1)}} for arbitrary l, where c
l
(Q) is an explicitly determined constant. This remains true for k = 3 under the restriction l ≤ 3. 相似文献
9.
We define a generalized Li coefficient for the L-functions attached to the Rankin–Selberg convolution of two cuspidal unitary automorphic representations π and π
′ of
GLm(\mathbbAF)GL_{m}(\mathbb{A}_{F})
and
GLm¢(\mathbbAF)GL_{m^{\prime }}(\mathbb{A}_{F})
. Using the explicit formula, we obtain an arithmetic representation of the n th Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
attached to
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
. Then, we deduce a full asymptotic expansion of the archimedean contribution to
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
and investigate the contribution of the finite (non-archimedean) term. Under the generalized Riemann hypothesis (GRH) on non-trivial
zeros of
L(s,pf×[(p)\tilde]f¢)L(s,\pi _{f}\times \widetilde{\pi}_{f}^{\prime })
, the nth Li coefficient
lp,p¢(n)\lambda _{\pi ,\pi ^{\prime }}(n)
is evaluated in a different way and it is shown that GRH implies the bound towards a generalized Ramanujan conjecture for
the archimedean Langlands parameters μ
π
(v,j) of π. Namely, we prove that under GRH for
L(s,pf×[(p)\tilde]f)L(s,\pi _{f}\times \widetilde{\pi}_{f})
one has
|Remp(v,j)| £ \frac14|\mathop {\mathrm {Re}}\mu_{\pi}(v,j)|\leq \frac{1}{4}
for all archimedean places v at which π is unramified and all j=1,…,m. 相似文献
10.
Y. C. Wang 《Acta Mathematica Hungarica》2012,135(3):248-269
Let Hk\mathcal{H}_{k} denote the set {n∣2|n,
n\not o 1 (mod p)n\not\equiv 1\ (\mathrm{mod}\ p) ∀ p>2 with p−1|k}. We prove that when
X\frac1120(1-\frac12k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X, almost all integers
n ? \allowbreak Hk ?(X, X+H]n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]} can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when
X\frac1120(1-\frac1k) +e\leqq H\leqq XX^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X, almost all integers n∈(X,X+H] can be represented as the sum of a prime and a k-th power of integer for k≧3. 相似文献
11.
Lin-Feng Wang 《Annals of Global Analysis and Geometry》2010,37(4):393-402
Let M be an n-dimensional complete non-compact Riemannian manifold, dμ = e
h
(x)dV(x) be the weighted measure and
\trianglem{\triangle_{\mu}} be the weighted Laplacian. In this article, we prove that when the m-dimensional Bakry–émery curvature is bounded from below by Ric
m
≥ −(m − 1)K, K ≥ 0, then the bottom of the Lm2{{\rm L}_{\mu}^2} spectrum λ1(M) is bounded by
l1(M) £ \frac(m-1)2K4,\lambda_1(M) \le \frac{(m-1)^2K}{4}, 相似文献
12.
In this paper, we investigate an eigenvalue problem of Dirichlet Laplacian on a bounded domain Ω in an n-dimensional Euclidean space R
n
. If λ
k+1 is the (k + 1)th eigenvalue of Dirichlet Laplacian on Ω, then, we prove that, for n ≥ 41 and
and, for any n and
with
, where j
p,k
denotes the k-th positive zero of the standard Bessel function J
p
(x) of the first kind of order p. From the asymptotic formula of Weyl and the partial solution of the conjecture of Pólya, we know that our estimates are optimal in the sense of order of k.Q.-M. Cheng was partially Supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of ScienceH. Yang was partially Supported by Chinese NSF, SF of CAS and NSF of USA 相似文献
13.
We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace
K
Θ=H
2⊖ΘH
2 of the Hardy space H
2, where Θ is an inner function. First, we verify the Feichtinger conjecture for the kernels [(k)\tilde]ln=kln/||kln||\tilde{k}_{\lambda_{n}}=k_{\lambda_{n}}/\|k_{\lambda _{n}}\| under the assumption that sup
n
|Θ(λ
n
)|<1. Second, we prove the Feichtinger conjecture in the case where Θ is a one-component inner function, meaning that the
set {z:|Θ(z)|<ε} is connected for some ε∈(0,1). 相似文献
14.
We study a necessary and sufficient condition for Jacobi integrals of weight
-r+\fracj2-r+\frac{j}{2}, r∈ℤ≥0, and index ℳ(j) on ℋ×ℂ
j
to have a dual Jacobi form of weight
r+\fracj2+2r+\frac{j}{2}+2 and index ℳ(j). Such a meromorphic Jacobi integral with a dual Jacobi form is called a mock Jacobi form whose concept was first introduced
by Zagier in Séminaire Bourbaki, 60éme année, 2006–2007, N° 986. In fact, we show the map Lr+1M(j)L^{r+1}_{\mathcal{M}^{(j)}} from the space of mock Jacobi forms to that of Jacobi forms is surjective by constructing the corresponding inverse image
via Eichler integral of vector valued modular forms which are coming from the theta decomposition of Jacobi forms. We discuss
Lerch sums as a typical example. 相似文献
15.
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
16.
M. Eie Y. L. Ong 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1997,67(1):149-157
Suppose thatm, n are positive even integers andp is a prime number such thatp-1 is not a divisor ofm. For any non-negative integerN, the classical Kummer’s congruences on Bernoulli numbersB
n(n = 1,2,3,...) assert that (1-p
m-1)B
m/m isp-integral and
17.
Bodo Dittmar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,95(1):565-568
For a simply connected and normalized domain D in the plane it was proven by Pólya and Schiffer in 1954 for the fixed membrane eigenvalues
|