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1.
2.
We establish a criterion for the existence of a solution of the interpolation problem f(
n
) = b
n in the class of functions f analytic in the unit disk and satisfying the relation
where : [1; +) (0; +) is an increasing function such that the function ln(t) is convex with respect to lnt on the interval [1; +) and lnt = o(ln(t)), t . 相似文献
3.
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition
$
\frac{{f(z)}}
{z} \ne 0and\left| {f'(z)\left( {\frac{z}
{{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.
$
\frac{{f(z)}}
{z} \ne 0and\left| {f'(z)\left( {\frac{z}
{{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.
相似文献
4.
O. B. Skaskiv 《Mathematical Notes》1999,66(2):223-232
For an entire Dirichlet series
, sufficient conditions on the exponents
are established such that the following relations hold outside a set of finite measure asx→+∞:
5.
We establish conditions for the existence of a solution of the interpolation problem f(
n
) = b
n in the class of functions f analytic in the unit disk and such that
6.
LiJunjie BianBaojun 《高校应用数学学报(英文版)》2000,15(3):273-280
The following regularity of weak solutions of a class of elliptic equations of the form are investigated. 相似文献
7.
We describe sequences of zeros of functions f 0 analytic in the half-plane
and satisfying the condition
where : [0; +) (0; +) is an increasing function such that the function ln (r) is convex with respect to ln r on [1; +). 相似文献
8.
Jacob Korevaar 《Journal d'Analyse Mathématique》2001,85(1):177-194
For entire functionsf whose power series have Hadamard gaps with ratio ≥1+α>1, Gaier has shown that the condition |f(x)|≤e
x forx≥0 implies |f(z)|≤C
αe|z| (*) for allz. Here the result is extended to the case of square root gaps, that is,
, with
, where α>0. Smaller gaps cannot work. In connection with his proof of the general high indices theorem for Borel summability,
Gaier had shown that square root gaps imply
. Having such an estimate, one can adapt Pitt’s Tauberian method for the restricted Borel high indices theorem to show that,
in fact,
, which implies (*). The author also states an equivalent distance formula involving monomialsx
pke−xinL
∞ (0, ∞). 相似文献
9.
Summary Let
be a sequence of independent identically distributed random variables withθ
1∼G and the conditional distribution ofx
1 givenθ
1=θ given by
. HereG is unknown andF
θ(·) is known. This paper provides estimators
ofG based onx
1, …,x
n such that the random variable sup
has an asymptotic distribution asn→∞ under certain on conditionsG and for certain choices ofF
θ. A simulation model has been discussed involving the uniform distribution on (0, θ) forF
θ and an exponential distribution forG.
Research supported by the National Science Foundation under Grant #MCS77-26809. 相似文献
10.
Let {X, X
n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set
. Suppose lim
n→∞
and
, where d=2, if −1<b<0 and d>2(b+1), if b≥0. It is proved that, for any b>−1,
11.
In this paper, we establish the existence and concentration of solutions of a class of nonlinear Schr?dinger equation $$- \varepsilon ^2 \Delta u_\varepsilon + V\left( x \right)u_\varepsilon = K\left( x \right)\left| {u_\varepsilon } \right|^{p - 2} u_\varepsilon e^{\alpha _0 \left| {u_\varepsilon } \right|^\gamma } , u_\varepsilon > 0, u_\varepsilon \in H^1 \left( {\mathbb{R}^2 } \right),$$ where 2 < p < ∞, α 0 > 0, 0 < γ < 2. When the potential function V (x) decays at infinity like (1 + |x|)?α with 0 < α ≤ 2 and K(x) > 0 are permitted to be unbounded under some necessary restrictions, we will show that a positive H 1(?2)-solution u ? exists if it is assumed that the corresponding ground energy function G(ξ) of nonlinear Schr?dinger equation $- \Delta u + V\left( \xi \right)u = K\left( \xi \right)\left| u \right|^{p - 2} ue^{\alpha _0 \left| u \right|^\gamma }$ has local minimum points. Furthermore, the concentration property of u ? is also established as ? tends to zero. 相似文献
12.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
13.
We consider the following singularly perturbed boundary-value problem:
14.
Let V(z) be a complex-valued function on the complex plane ℂ satisfying the condition |V(z) − V(ζ)| ≤ w|z − ζ|, z, ζ ε ℂ; ω ≥ 0 be a Muckenhoupt A
p
weight on ℂ; i.e., the inequality
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