共查询到20条相似文献,搜索用时 46 毫秒
1.
We consider the weighted Bergman spaces
HL2(\mathbb Bd, ml){\mathcal {H}L^{2}(\mathbb {B}^{d}, \mu_{\lambda})}, where we set dml(z) = cl(1-|z|2)l dt(z){d\mu_{\lambda}(z) = c_{\lambda}(1-|z|^2)^{\lambda} d\tau(z)}, with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators
on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which
the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert–Schmidt operators on the generalized
Bergman spaces. 相似文献
2.
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
3.
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
4.
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
5.
L. V. Rozovsky 《Journal of Mathematical Sciences》2003,118(6):5624-5634
Let X1, X2, ... be i.i.d. random variables satisfying the condition
|