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1.
E. G. Goluzina 《Journal of Mathematical Sciences》1997,83(6):745-749
Let Mk,λ(0≤λ≤1, k≥2) be the class of functions f(z)=1/z+ao+a1z+... that are regular and locally univalent for 0<⩛z⩛<1 and satisfy the condition
where Jλ(z)=λ(1+zf″(z)/f'(z))+(1-λ)zf'(z)/f(z). In the class Mk,λ we consider sorne coefficient problems and problems concerning distortion theorems.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 212, 1994, pp. 91–96.
Translated by N. Yu. Netsvetaev. 相似文献
2.
R. V. Hrushevoi 《Ukrainian Mathematical Journal》2008,60(4):540-550
We describe the set
of parameters γ for which there exists a decomposition of the operator γI
H in a sum of n self-adjoint operators with spectra from the sets M
1, …, M
n, M
i = 0, 1, …, k
i, for n ≥ 4 and, in some cases, for n = 3.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 470–477, April, 2008. 相似文献
3.
If w1,…,w
N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ1,…, λN on the unit circle and positive numbers Μ1,…,Μ
N such that
is the zero sequence of the function 1 —
. The points λ1,…, λN and numbers Μ1,…,ΜN are unique (except for reorderings). 相似文献
4.
A. V. Bogomol'naya 《Journal of Mathematical Sciences》1995,73(6):633-637
We consider
,mE > 0,G(E) is a certain subspace of L
1
(E) consisting of functions concentrated on E and integrable, and {dk}, (k ∈ ℤ) in a summable sequence of positive numbers. It is proved that if G(E)=Lp(E), p≥2, then there exists f∈G(E) such that |f(n)|≥dn,
(one of the questions involved in the majorization problem). Sufficient conditions are obtained for certain other function
classes G(E). We study the question of partial majorization. Bibliography: 2 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 13, 1992, pp. 42–48. 相似文献
5.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
wherea
i
≠0 is integer,i=1,2…,s. In 1979, Schmidt proved that if ∈>0 then there is a large constantC(k,∈) such that fors>C(k,∈) the equationf(X)=0 has a nontrivial, integer solution in σ1, σ2, …, σ3,x
1,x
2, …,x
3 satisfying
Schmidt did not estimate this constantC(k,∈) since it would be extremely large. In this paper, we prove the following result 相似文献
6.
Amitai Regev 《Israel Journal of Mathematics》1999,113(1):15-28
The numbers
% MathType!End!2!1!, λ ⊢n appear in the enumeration of various objects, as well as coefficients inS
nrepresentations associated with products of higher commutators. We study their asymptotics asn→∞ and show that if (λ1, λ2, …)≈(α
1,α
2, …)n, if (λ′1, λ′2, …)≈(β
1,β
2, …)n and ifγ=1− Σ
k⩽1(α
k⩽1+β
k⩽1), then
% MathType!End!2!1!.
Work partially supported by N.S.F. Grant No. DMS 94-01197. 相似文献
7.
S. V. Astashkin 《Mathematical Notes》1999,65(4):407-417
In this paper it is proved that from any uniformly bounded orthonormal system {f
n}
n=1
∞
of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni}
i
Emphasis>=1/∞
majorized in distribution by the Rademacher system on [0, 1]. This means that {
}, whereC>0 is independent of m∈N, ai∈N (i=1,…,m) andz>0.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 483–495, April, 1999. 相似文献
8.
I. I. Sharapudinov 《Mathematical Notes》2000,67(3):389-397
Let
N+2m
={−m, −m+1, …, −1, 0, 1, …,N−1,N, …,N−1+m}. The present paper is devoted to the approximation of discrete functions of the formf :
N+2m
→ ℝ by algebraic polynomials on the grid Ω
N
={0, 1, …,N−1}. On the basis of two systems of Chebyshev polynomials orthogonal on the sets Ω
N+m
and Ω
N
, respectively, we construct a linear operatorY
n+2m, N
=Y
n+2m, N
(f), acting in the space of discrete functions as an algebraic polynomial of degree at mostn+2m for which the following estimate holds (x ε Ω
N
):
whereE
n+m[g,l
2(Ω
N+m
)] is the best approximation of the function
by algebraic polynomials of degree at mostn+m in the spacel
2 (Ω
N+m
) and the function Θ
N, α
(x) depends only on the weighted estimate for the Chebyshev polynomialsτ
k
α,α
(x, N).
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 460–470, March, 2000. 相似文献
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9.
Zamira Abdikalikova Ryskul Oinarov Lars-Erik Persson 《Czechoslovak Mathematical Journal》2011,61(1):7-26
We consider a new Sobolev type function space called the space with multiweighted derivatives $
W_{p,\bar \alpha }^n
$
W_{p,\bar \alpha }^n
, where $
\bar \alpha
$
\bar \alpha
= (α
0, α
1,…, α
n
), α
i
∈ ℝ, i = 0, 1,…, n, and $
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
$
\left\| f \right\|W_{p,\bar \alpha }^n = \left\| {D_{\bar \alpha }^n f} \right\|_p + \sum\limits_{i = 0}^{n - 1} {\left| {D_{\bar \alpha }^i f(1)} \right|}
,
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
$
D_{\bar \alpha }^0 f(t) = t^{\alpha _0 } f(t),D_{\bar \alpha }^i f(t) = t^{\alpha _i } \frac{d}
{{dt}}D_{\bar \alpha }^{i - 1} f(t),i = 1,2,...,n
相似文献
10.
Piotr Niemiec 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):391-399
The aim of the paper is to prove that every f ∈ L
1([0,1]) is of the form f = , where j
n,k
is the characteristic function of the interval [k- 1 / 2
n
, k / 2
n
) and Σ
n=0∞Σ
k=12n
|a
n,k
| is arbitrarily close to ||f|| (Theorem 2). It is also shown that if μ is any probabilistic Borel measure on [0,1], then for any ɛ > 0 there exists a sequence (b
n,k
)
n≧0
k=1,...,2n
of real numbers such that and for each Lipschitz function g: [0,1] → ℝ (Theorem 3).
相似文献
11.
O. M. Fomenko 《Journal of Mathematical Sciences》2006,133(6):1733-1748
Let Sk(Γ) be the space of holomorphic Γ-cusp forms f(z) of even weight k ≥ 12 for Γ = SL(2, ℤ), and let Sk(Γ)+ be the set of all Hecke eigenforms from this space with the first Fourier coefficient af(1) = 1. For f ∈ Sk(Γ)+, consider the Hecke L-function L(s, f). Let
12.
E. G. Goluzina 《Journal of Mathematical Sciences》1996,79(5):1304-1307
We study the structural properties of the class Mk,λ,b(k≥2, 0≤λ≤1, b∈ℂ\{0}) of functions f(z)=z+ ... which are regular in |z|<1 and satisfy the conditions f(z)f′(z)z−1≠0 and
, where J(z)=λ(1+b−1zf″(z)/f′(z)+(1−λ)(b−1zf′(z)/f(z)+1−b−1). The value regions of some functionals on this class are found. The case λ=1 was considered in our previous paper. Bibliography:
4 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 55–60.
Translated by O. A. Ivanov. 相似文献
13.
V. V. Rimatskii 《Algebra and Logic》1996,35(5):344-349
In the present article, we prove the theorem which states that every table modal logic λ of depth 2 over S4 has a finite basis
of admissible inference rules. In addition, it is established that a finite algebra ℒ belongs to Fω(λ)Q iff there exist numbers n1…, nk such that
(Lemma 5). Let F be a λ-frame of depth 2 and b a cluster of the second layer in F. We show that for any n1,…,nk, there exist no p-morphisms from (Fn1⊔…⊔Fnk)+ a local component K (b) such that, for any n, there is no p-morphism from any local component of Fn onto K (b) (Lemma 6).
Translated fromAlgebra i Logika, Vol. 35, pp. 612–622, September–October, 1996. 相似文献
14.
刘新和 《高校应用数学学报(英文版)》2003,18(2):129-137
§ 1 IntroductionThe Feigenbaum functional equation plays an importantrole in the theory concerninguniversal properties of one-parameter families of maps of the interval that has the formf2 (λx) +λf(x) =0 ,0 <λ=-f(1 ) <1 ,f(0 ) =1 ,(1 .1 )where f is a map ofthe interval[-1 ,1 ] into itself.Lanford[1 ] exhibited a computer-assist-ed proof for the existence of an even analytic solution to Eq.(1 .1 ) .It was shown in[2 ]that Eq.(1 .1 ) does not have an entire solution.Si[3] discussed the it… 相似文献
15.
Two Inequalities for Convex Functions 总被引:1,自引:0,他引:1
Let a 0 < a 1 < ··· < a n be positive integers with sums $ {\sum\nolimits_{i = 0}^n {\varepsilon _{i} a_{i} {\left( {\varepsilon _{i} = 0,1} \right)}} }
16.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
17.
We observe an unknown function of infinitely many variables f = f(t), t = (t1, ..., tn, ... ) ∈, [0, 1]∞, in the Gaussian white noise of level ε > 0. We suppose that in each variable there exists a 1-periodical σ-smooth extension
of the function f(t) to IR
∞. Taking a quantity σ > 0 and a positive sequence a = {ak}, we consider the set
that consists of functions f such that
. We consider the cases ak = kα and ak = exp(λk), α > 0, λ > 0. We would like to estimate a function f ∈
or to test the null hypothesis H0: f = 0 against the alternatives f ∈
, where the set
consists of functions f ∈
such that ∥f∥2 ≥ r. In the estimation problem, we obtain the asymptotics (as ε → 0) of the minimax quadratic risk. In the detection problem,
we study the sharp asymptotics of minimax separation rates f
ɛ
*
that provide distiguishability in the problems. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 91–113. 相似文献
18.
Take a linear ordinary differential operator $\mathfrak{d}\left( z \right) = \sum\nolimits_{i = 1}^k {Q_i \left( z \right)\frac{{d^i }}
{{dz^i }}}$\mathfrak{d}\left( z \right) = \sum\nolimits_{i = 1}^k {Q_i \left( z \right)\frac{{d^i }}
{{dz^i }}} with polynomial coefficients and set r = max
i=1,…,k(deg Q
i
(z) − i). If d(z) satisfies the conditions: (i) r ≥ 0 and (ii) deg Q
k
(z) = k + r, we call it a non-degenerate higher Lamé operator. Following the classical examples of E. Heine and T. Stieltjes we initiated in [13] the study of the following multiparameter spectral problem: for each positive integer n find polynomials V (z) of degree at most r such that the equation
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