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1.
I. I. Sharapudinov 《Mathematical Notes》1997,62(4):501-512
Suppose that 0<δ≤1,N=1/δ, and α, ga≥0, is an integer. For the classical Meixner polynomials
orthonormal on the gird {0, δ, 2δ, ...} with weight ρ(x)=(1-e
−δ)αг(Nx+α+ 1)/г(Nx+1), the following asymptotic formula is obtained:
. The remainderv
n,N
α
(z) forn≤λN satisfies the estimate
where Λ
k
α
(x) are the Laguerre orthonormal polynomials. As a consequence, a weighted estimate, for the Meixner polynomial
on the semiaxis [0, ∞) is obtained.
Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 603–616, October, 1997.
Translated by N. K. Kulman 相似文献
2.
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
3.
The existence of the singular integral ∫K(x, y)f(y)dy associated to a Calderón-Zygmund kernel where the integral is understood
in the principal value sense TF(x)=limε→0+∫|x−y|>εK(x, y)f(y)dy has been well studied. In this paper we study the existence of the above integral in the Cesàro-α sense. More
precisely, we study the existence of
for −1<α<0 in the setting of weighted spaces. 相似文献
4.
Let {xn}n∈ℕ be a sequence in [0, 1]d , {λn}n∈ℕ a sequence of positive real numbers converging to 0, and δ > 1. The classical ubiquity results are concerned with the computation of the Hausdorff dimension of limsup-sets of the form
Let μ be a positive Borel measure on [0, 1]d , ρ 2 (0, 1] and α > 0. Consider the finer limsup-set
We show that, under suitable assumptions on the measure μ, the Hausdorff dimension of the sets Sμ(ρ, δ, α) can be computed. Moreover, when ρ < 1, a yet unknown saturation phenomenon appears in the computation of the Hausdorff dimension of Sμ(ρ, δ, α). Our results apply to several classes of multifractal measures, and S(δ) corresponds to the special case where μ is a monofractal measure like the Lebesgue measure.
The computation of the dimensions of such sets opens the way to the study of several new objects and phenomena. Applications
are given for the Diophantine approximation conditioned by (or combined with) b-adic expansion properties, by averages of some Birkhoff sums and branching randomwalks, as well as by asymptotic behavior
of random covering numbers. 相似文献
5.
A. L. Treskunov 《Journal of Mathematical Sciences》2000,101(2):3025-3048
Sharp two-sided estimates are obtained for the eigenvalues\Gl
n
of the problem
, where a(x), b(x), c(x), and g(x) are bounded measurable functions satisfying the conditions v ⩽ a(x)ξ2 + 2b(x)+η+c(x)η2⩽1,v>0,ξ2+η2=1,|g(x)|⩽δ,δ⩾0. For fixed ν>0 and δ≥0 we have the following exact inequalities:
. In the special case of the problem (0.1) (a(x)≡b(x) and b(x)≡0), sharp two-sided estimates are also proved. Bibliography:
6 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 19, 1999, pp. 215–243. 相似文献
6.
A. Michael Alphonse 《Journal of Fourier Analysis and Applications》2000,6(4):449-456
In this paper we prove that the maximal commutator of singular integral operator [b, T]* satisfies the inequality:
where f is any smooth function with compact support, λ>0 and C is a positive constant independent of f and λ. 相似文献
7.
Ahmet Yıldız Cengizhan Murathan Kadri Arslan Rıdvan Ezentaş 《Monatshefte für Mathematik》2007,151(3):247-256
Let
be (2n + 1)-dimensional Sasakian space form of constant ϕ-sectional curvature (c) and M
n
be an
n
-dimensional C-totally real, minimal submanifold of
. We prove that if M
n
is pseudo-parallel and
, then M
n
is totally geodesic. 相似文献
8.
Asymptotic behavior of the spectrum of a pseudodifferential operator with periodic bicharacteristics
Yu. G. Safarov 《Journal of Mathematical Sciences》1988,40(5):645-652
Let j be the eigenvalues of a positive elliptic pseudodifferential operator of order m > 0 on a closed compact d-dimensional C-manifold and let N()=#{j:jm}. It is shown that for each > 0 we have
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相似文献
9.
G. Kuba 《Archiv der Mathematik》2002,79(6):534-542
Let
(z ∈ ℝ). Further let λ denote a large real parameter. We show that for arbitrary real numbersk and α withk>=2.7013 and 0<α≦1,
10.
Chen Hua 《数学学报(英文版)》1997,13(1):81-89
In this paper, we study the asymptotic behaviour of the scattering phases(λ) of the Dirichlet Laplacian associated with obstacle
, where Ω is a bounded open subset of ℝ
n
(n≥2) with non-smooth boundary ∂Ω and connected complement Ω
e
=ℝ
n
. We can prove that if Ω satisfies a certain geometrical condition, then
11.
Let II be a bounded symmetric domain, ω ⇉ I a bounded subdomain, and let
denote the weighted Bergman space of holomorphic square integrable functions on I. Let Tλ, ω be the Berezin-Toeplitz operator on
with symbol χΩ and kth eigenvalue λ
k
(T
λ,Ω). We prove that for δ1 sufficiently close to 0 and δ2 sufficiently close to 1 the estimate
12.
By using different convex functionals to compute fixed point index, the existence of positive solutions for a class of second-order
two-point boundary value problem
13.
In this paper we consider the existence and asymptotic behavior of solutions of the following problem:
14.
Zhian Wang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):399-418
We derive the optimal decay rates of solution to the Cauchy problem for a set of nonlinear evolution equations with ellipticity
and dissipative effects
15.
Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:
16.
I. M. Guseinov 《Mathematical Notes》1997,62(2):172-180
We prove the existence of a transformation operator that takes the solution of the equationy″=λ2n
y to the solution of the equation
17.
Teresa D'Aprile Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2006,25(1):105-137
We study the following system of Maxwell-Schrödinger equations $ \Delta u - u - \delta u \psi+ f(u)=0, \quad \Delta \psi + u^2 = 0 \mbox{in} {\mathbb R}^N , u, \;\psi > 0, \quad u, \;\psi \to 0 \ \mbox{as} \ |x| \to + \infty, $ where δ > 0, u, ψ : $\psi: {\mathbb R}^N \to {\mathbb R}
18.
We study the complexity of a noninterior path-following method for the linear complementarity problem. The method is based on the Chen–Harker–Kanzow–Smale smoothing function. It is assumed that the matrix M is either a P-matrix or symmetric and positive definite. When M is a P-matrix, it is shown that the algorithm finds a solution satisfying the conditions Mx-y+q=0 and
in at most
19.
Cristinel Mortici 《Archiv der Mathematik》2009,93(1):37-45
We prove in this paper that for every x ≥ 0,
20.
V. M. Buchstaber V. Z. Enolskii D. V. Leykin 《Functional Analysis and Its Applications》2000,34(3):159-171
We obtain an explicit realization of the Jacobi and Kummer varieties for trigonal curves of genusg (gcd(g,3)=1) of the form
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