共查询到20条相似文献,搜索用时 31 毫秒
1.
Let
W í \Bbb C\Omega \subseteq {\Bbb C}
be a simply connected domain in
\Bbb C{\Bbb C}
, such that
{¥} è[ \Bbb C \[`(W)]]\{\infty\} \cup [ {\Bbb C} \setminus \bar{\Omega}]
is connected. If g is holomorphic in Ω and every derivative of g extends continuously on
[`(W)]\bar{\Omega}
, then we write g ∈ A∞ (Ω). For g ∈ A∞ (Ω) and
z ? [`(W)]\zeta \in \bar{\Omega}
we denote
SN (g,z)(z) = ?Nl=0\fracg(l) (z)l ! (z-z)lS_N (g,\zeta )(z)= \sum^{N}_{l=0}\frac{g^{(l)} (\zeta )}{l !} (z-\zeta )^l
. We prove the existence of a function f ∈ A∞(Ω), such that the following hold:
相似文献
i) | There exists a strictly increasing sequence μn ∈ {0, 1, 2, …}, n = 1, 2, …, such that, for every pair of compact sets Γ, Δ ⊂ [`(W)]\bar{\Omega} and every l ∈ {0, 1, 2, …} we have supz ? G supw ? D \frac?l?wl Smn ( f,z) (w)-f(l)(w) ? 0, as n ? + ¥ and\sup_{\zeta \in \Gamma} \sup_{w \in \Delta} \frac{\partial^l}{\partial w^l} S_{\mu_ n} (\,f,\zeta) (w)-f^{(l)}(w) \rightarrow 0, \hskip 7.8pt {\rm as}\,n \rightarrow + \infty \quad {\rm and} |
ii) | For every compact set K ì \Bbb CK \subset {\Bbb C} with K?[`(W)] = ?K\cap \bar{\Omega} =\emptyset and Kc connected and every function h: K? \Bbb Ch: K\rightarrow {\Bbb C} continuous on K and holomorphic in K0, there exists a subsequence { m¢n }¥n=1\{ \mu^\prime _n \}^{\infty}_{n=1} of {mn }¥n=1\{\mu_n \}^{\infty}_{n=1} , such that, for every compact set L ì [`(W)]L \subset \bar{\Omega} we have supz ? L supz ? K Sm¢n ( f,z)(z)-h(z) ? 0, as n? + ¥.\sup_{\zeta \in L} \sup_{z\in K} S_{\mu^\prime _n} (\,f,\zeta )(z)-h(z) \rightarrow 0, \hskip 7.8pt {\rm as} \, n\rightarrow + \infty . |
2.
Hengcai Tang 《Archiv der Mathematik》2013,100(2):123-130
Let f(z) be a holomorphic Hecke eigenform of even weight k for the full modular group ${SL_2(\mathbb{Z})}$ , and denote by L(s, sym2 f) the corresponding symmetric square L-function associated to f. Suppose that ${\lambda_{\rm{sym}^2} f(n)}$ is the nth normalized Fourier coefficient of L(s, sym2 f). In this paper, the asymptotic formula $$\begin{array}{ll}\sum_{n\leq x} \lambda^2_{\rm{sym}^2 f}(n) = C x + O(x^{\frac{10}{13}} \log^{9} x)\end{array}$$ is established. 相似文献
3.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}The aim of this study is to prove global existence of classical solutions for systems of the form
\frac?u?t -a Du=-f(u,v){\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)} ,
\frac?v?t -b Dv=g(u,v){\frac{\partial v}{\partial t} -b \Delta v=g(u,v)} in (0, +∞) × Ω where Ω is an open bounded domain of class C
1 in
\mathbbRn{\mathbb{R}^n}, a > 0, b > 0 and f, g are nonnegative continuously differentiable functions on [0, +∞) × [0, +∞) satisfying f (0, η) = 0, g(x,h) £ C j(x)eahb{g(\xi,\eta) \leq C \varphi(\xi)e^{\alpha {\eta^\beta}}} and g(ξ, η) ≤ ψ(η)f(ξ, η) for some constants C > 0, α > 0 and β ≥ 1 where j{\varphi} and ψ are any nonnegative continuously differentiable functions on [0, +∞) such that j(0)=0{\varphi(0)=0} and limh? +¥hb-1y(h) = l{ \lim_{\eta \rightarrow +\infty}\eta^{\beta -1}\psi(\eta)= \ell} where ℓ is a nonnegative constant. The asymptotic behavior of the global solutions as t goes to +∞ is also studied. For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates
and Lyapunov functional methods. 相似文献
4.
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
5.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
\Bbb C{\Bbb C}
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
Cn(W,P) := supf ? A(W,P)supz ? W\frac|f(n)(z)| R(f(z),P)n! (R(z,W))nC_n(\Omega,\Pi)\,:=\,\sup_{f\in A(\Omega,\Pi)}\sup_{z\in \Omega}\frac{\vert f^{(n)}(z)\vert\,R(f(z),\Pi)}{n!\,(R(z,\Omega))^n}
are finite for all
n ? \Bbb N{n \in {\Bbb N}}
if and only if ∂Ω and ∂Π do not contain isolated points. 相似文献
6.
Bart De Bruyn 《Annals of Combinatorics》2010,14(3):307-318
Let f be an isometric embedding of the dual polar space ${\Delta = DQ(2n, {\mathbb K})}Let f be an isometric embedding of the dual polar space
D = DQ(2n, \mathbb K){\Delta = DQ(2n, {\mathbb K})} into
D¢ = DQ(2n, \mathbb K¢){\Delta^\prime = DQ(2n, {\mathbb K}^\prime)}. Let P denote the point-set of Δ and let
e¢: D¢? S¢ @ PG(2n - 1, \mathbb K¢){e^\prime : \Delta^\prime \rightarrow {\Sigma^\prime} \cong {\rm PG}(2^n - 1, {{\mathbb K}^\prime})} denote the spin-embedding of Δ′. We show that for every locally singular hyperplane H of Δ, there exists a unique locally singular hyperplane H′ of Δ′ such that f(H) = f(P) ?H¢{f(H) = f(P) \cap H^\prime}. We use this to show that there exists a subgeometry
S @ PG(2n - 1, \mathbb K){\Sigma \cong {\rm PG}(2^n - 1, {\mathbb K})} of Σ′ such that: (i) e¢°f (x) ? S{e^\prime \circ f (x) \in \Sigma} for every point x of D; (ii) e : = e¢°f{\Delta; ({\rm ii})\,e := e^\prime \circ f} defines a full embedding of Δ into Σ, which is isomorphic to the spin-embedding of Δ. 相似文献
7.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 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
limN ? ¥ || sNd (f) - f ||p0 = 0\mathop {\lim }\limits_{N \to \infty } \left\| {\sigma _N^\delta (f) - f} \right\|p_0 = 0 相似文献
9.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}
10.
Huixue LAO 《数学年刊B辑(英文版)》2012,33(6):877-888
Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full modular group. Let ?? f (n) be the nth normalized Fourier coefficient of f(z). Suppose that L(sym2 f, s) is the symmetric square L-function associated with f(z), and $ \lambda _{sym^2 f} (n) $ (n) denotes the nth coefficient L(sym2 f, s). In this paper, it is proved that $$ \sum\limits_{n \leqslant x} {\lambda _{sym^2 f}^4 (n)} = xP2(\log x) + O(x^{\frac{{79}} {{81}} + \varepsilon } ), $$ , where P 2(t) is a polynomial in t of degree 2. Similarly, it is obtained that $$ \sum\limits_{n \leqslant x} {\lambda _f^4 (n^2 )} = x\tilde P2(\log x) + O(x^{\frac{{79}} {{81}} + \varepsilon } ), $$ , where $ \tilde P_2 (t) $ is a polynomial in t of degree 2. 相似文献
11.
Let f be a cusp form of the Hecke space
\frak M0(l,k,e){\frak M}_0(\lambda,k,\epsilon)
and let L
f
be the normalized L-function associated to f. Recently it has been proved that L
f
belongs to an axiomatically defined class of functions
[`(S)]\sharp\bar{\cal S}^\sharp
. We prove that when λ ≤ 2, L
f
is always almost primitive, i.e., that if L
f
is written as product of functions in
[`(S)]\sharp\bar{\cal S}^\sharp
, then one factor, at least, has degree zeros and hence is a Dirichlet polynomial. Moreover, we prove that if
l ? {?2,?3,2}\lambda\notin\{\sqrt{2},\sqrt{3},2\}
then L
f
is also primitive, i.e., that if L
f
= F
1
F
2 then F
1 (or F
2) is constant; for
l ? {?2,?3,2}\lambda\in\{\sqrt{2},\sqrt{3},2\}
the factorization of non-primitive functions is studied and examples of non-primitive functions are given. At last, the subset
of functions f for which L
f
belongs to the more familiar extended Selberg class
S\sharp{\cal S}^\sharp
is characterized and for these functions we obtain analogous conclusions about their (almost) primitivity in
S\sharp{\cal S}^\sharp
. 相似文献
12.
Vladimir Varlamov 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2010,138(6):1017-1031
Riesz fractional derivatives are defined as fractional powers of the Laplacian, D α = (?Δ) α/2 for ${\alpha \in \mathbb{R}}
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |