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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.
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→+∞:
, where ψ(x) is a function increasing to +∞ and such thatx≤ψ(x)≤e x (x≥0). Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 282–292, August, 1999  相似文献   

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
0} \right)\;\left( {\forall z,\;|\;z\;| < 1} \right):\;\;\left| {f\left( z \right)} \right|\;\; \leqslant \;\;\;\exp \left( {c_1 \eta \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right).$$ " align="middle" vspace="20%" border="0">
Here, : [1; +) (0; +) is an increasing function convex with respect to lnt on the interval [1; +) and such that lnt = o((t)), t .  相似文献   

6.
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.
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,
, where Γ(•) is a Gamma function. Research supported by the National Natural Science Foundation of China (10071072).  相似文献   

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.
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:
on the interval 0 ≤x ≤ 1. We study the existence and uniqueness of its solutionu(x, ε) having the following properties:u(x, ε) →u 0(x) asε → 0 uniformly inx ε [0, 1], whereu 0(x) εC [0, 1] is a solution of the degenerate equationf(x, u, u′)=0; there exists a pointx 0 ε (0, 1) such thata(x 0)=0,a′(x 0) > 0,a(x) < 0 for 0 ≤x <x 0, anda(x) > 0 forx 0 <x ≤ 1, wherea(x)=f′ v(x,u 0(x),u′ 0(x)). Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 520–524, April, 2000.  相似文献   

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
$ \left( {\frac{1} {{\left| B \right|}}\int\limits_B {\omega d\sigma } } \right)\left( {\frac{1} {{\left| B \right|}}\int\limits_B {\omega ^{ - \frac{1} {{p - 1}}} d\sigma } } \right)^{p - 1} \leqslant c_0 $ \left( {\frac{1} {{\left| B \right|}}\int\limits_B {\omega d\sigma } } \right)\left( {\frac{1} {{\left| B \right|}}\int\limits_B {\omega ^{ - \frac{1} {{p - 1}}} d\sigma } } \right)^{p - 1} \leqslant c_0   相似文献   

15.
For Banach space operators T satisfying the Tadmor-Ritt condition a band limited H calculus is established, where and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus, These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived. Received: 25 October 2004; revised: 31 January 2005  相似文献   

16.
In this paper, the existence “in the large” of time-periodic classical solutions (with period T) is proved for the following two dissipative ε-approximations for the Navier-Stokes equations modified in the sense of O. A. Ladyzhenskaya:
(1)
(1)
and the following two dissipative ε-approximations for the equations of motion of the Kelvin-Voight fluids: satisfying the free surface conditions on the boundary ϖΩ of a domain Ω⊂R3:
. The free term f(x, t) in systems (1)–(4) is assumed to be t-periodic with period T. It is shown that as ε→0, the classical t-periodic solutions (with period T) of Eqs. (1)–(4) satisfying the free surface conditions (5) converge to the classicat t-periodic solutions (with period T) of the Navier-Stokes equations modified in the sense of O. A. Ladyzhenskaya and to the equations of motion of the Kelvin-Voight fruids, respectively, satisfying the boundary condition (5). Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 109–124. Translated by N. S. Zabavnikova.  相似文献   

17.
We prove the existence of a positive and smooth solution for the following semilinear elliptic problem: % MathType!End!2!1! for anyaR N , 1<p<1+2/N andq=(p+1)/2. This solution decays exponentially as |x|→+∞. Moreover, if |a| is sufficiently small, this positive and rapidly decaying solution is unique. The existence of a positive, self-similar solution % MathType!End!2!1! follows for the following convection-diffusion equation with absorption: % MathType!End!2!1!. It is also a very singular solution. This solution decays as |x|→+∞ for anyt>0 fixed. Because of the nonvariational nature of the elliptic problem, a fixed point method is used for proving the existence result. The uniqueness is proved applying the Implicit Function Theorem. The work of the first author has been partially supported by Grant 1273/00003/88 of the University of the Basque Country. The work of the second author has been supported by Grant PB 86-0112-C02-00 of the Dirección General de Investigación Científica y Técnica.  相似文献   

18.
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of . If E *(t)=E(t)-2πΔ*(t/2π) with , then we obtain
and
It is also shown how bounds for moments of | E *(t)| lead to bounds for moments of .  相似文献   

19.
A power series with radius of convergence equal 1 is called a (p,A)-lacunary one if nk ≥ Akp, A > 0, 1 < p < ∞. It is proved that if 1 < p < 2 and f(x) is a (p,A)-lacunary series that satisfies the condition
, where
, for some ε > 0, then f ≡ 0. We construct a (p,A)-lacunary series f 0 such that
with a constant C0 = C0(p,A) > 0. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2003, pp. 135–149.  相似文献   

20.
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and , we prove that
*Supported by the Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. 20060237 and 20050494).  相似文献   

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