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1.
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
2.
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
3.
Mats Andersson 《Journal d'Analyse Mathématique》1996,68(1):39-58
LetG
1,…,Gm be bounded holomorphic functions in a strictly pseudoconvex domainD such that
. We prove that for each
(0,q)-form ϕ inL
p(∂D), 1<p<∞, there are
formsu
1, …,u
m inL
p(∂D) such that ΣG
juj=ϕ. This generalizes previous results forq=0. The proof consists in delicate estimates of integral representation formulas of solutions and relies on a certainT1 theorem due to Christ and Journé. For (0,n−1)-forms there is a simpler proof that also gives the result forp=∞. Restricted to one variable this is precisely the corona theorem.
The author was partially supported by the Swedish Natural Research Council. 相似文献
4.
Dong Sheng Kang 《数学学报(英文版)》2009,25(3):435-444
Suppose Ω belong to R^N(N≥3) is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ:=((N-1)/2)^2,0≤μi〈(√μ-ai)^2,ai〈bi〈ai+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k(-div(|x-ξi|^-2ai△↓u)-μiu/|x-ξi|^2(1+ai)-u^pi-1/|x-ξi|^bipi)=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k. 相似文献
5.
J. C. Gupta 《Proceedings Mathematical Sciences》2000,110(4):415-430
Let G
n,k
be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencesc
n(β1,β2,…, β
k
), β1,β2,…, βk
= 0,1,2,…, β1+β2 + … +β
k
≤n,c
n(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + β
k
) where Δc
n(β1,β2,…, β
k
) =c
n(β1 + 1, β2,…, β
k
)+c
n(β1,β2+1,…, β
k
)+…+c
n (β1,β2,…, β
k
+1) -c
n(β1,β2,…, β
k
). Further, let Π
n,k
be the set of all symmetric probabilities on {0,1,2,…,k}
n
. We establish a one-to-one correspondence between the sets G
n,k
and Π
n,k
and use it to formulate and answer interesting questions about both. Assigning to G
n,k
the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, β
k
), 1 ≤ Σβ
i
≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σ
m
]; the centering constantsc
0(β1, β2,…, β
k
) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inR
k. 相似文献
6.
V. G. Zhuravlev 《Journal of Mathematical Sciences》2006,137(2):4658-4672
For the two-dimensional torus
, we construct the Rauzy tilings d0 ⊃ d1 ⊃ … ⊃ dm ⊃ …, where each tiling dm+1 is obtained by subdividing the tiles of dm. The following results are proved. Any tiling dm is invariant with respect to the torus shift S(x) = x+
mod ℤ2, where ζ−1 > 1 is the Pisot number satisfying the equation x3− x2−x-1 = 0. The induced map
is an exchange transformation of Bmd ⊂
, where d = d0 and
. The map S(m) is a shift of the torus
, which is affinely isomorphic to the original shift S. This means that the tilings dm are infinitely differentiable. If ZN(X) denotes the number of points in the orbit S1(0), S2(0), …, SN(0) belonging to the domain Bmd, then, for all m, the remainder rN(Bmd) = ZN(Bmd) − N ζm satisfies the bounds −1.7 < rN(Bmd) < 0.5. Bibliography: 10 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 83–106. 相似文献
7.
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
8.
The asymptotic expressions of the covariance matrices for both the least square estimates
L
α
T
and Markov (best linear) estimates
are obtained, based on a sample in a finite interval (0, T) of the regression co-efficients α = (α
1, …, α
m
0)′ of a parameter-continuous process with a stationary residual. We assume that the regression variables φ
ν(t), t ⩾ 0, ν = 1, …, m
0, are continuous in t, and satisfy conditions (3.1)–(3.3). For the residual, we assume that it is a stationary process that possesses a bounded
continuous spectral density f(λ). Under these assumptions, it is proven that
9.
Markus Brodmann 《manuscripta mathematica》1992,76(1):181-192
Let M be a generalized Cohen-Macaulay module over a noetherian local ring (R,m). Fix a standard system x1, …, xd∈m with respect to M and let
. We construct a coherent Cohen-Macaulay sheafK over the projective space ℙ
R/I
d-1
whose cohomological Hilbert functions depend only on the lengths of the local cohomology modules H
m
i
(M), (i=0, …, d−1). 相似文献
10.
K. N. Venkataraman K. Suresh Chandra 《Annals of the Institute of Statistical Mathematics》1984,36(1):101-118
Summary LetX(t) be a linear autoregressively generated explosive time series, with autoregressive coefficientsb
1,…,bq, and a constant termb
0, and an error term
; a0=1. Where ε(t),t≧1 are independent, Eε(t)=0, and Eε
2(t)=σ2 is positive and finite. In this paper two categories of
-consisent and asymptotically singularly normal estimators are proposed for (b
1,…,bq, b0) thus settling an open problem since the publication of the paper (Venkataraman [5]). Based on these estimators several additional
limit theorems based on estimated error residuals are proved. The parameter-free limit theorems of Spectral and Quenouille
types of this paper serve as asymptotic goodness of fit tests for the model generatingX(t). 相似文献
11.
In this paper, we investigate the complex oscillation of the differential equation
12.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
13.
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
):
14.
We study polymodal logics with n modal connectives □1,...,□n, each of which satisfies the axioms of S5 and, moreover, obeys the commutativity laws
. The following results are proved: (1) the logic S5nC is not locally finite; (2) the inference rule A(p1, …, pm)/B(p1, …, pm) is not admissible in
, and on a one-element model ∉, there exists a valuation of variables p1, …, pm, such that ∉ ⊪ A.
Supported by RFFR grant No. 96-01-00228.
Translated fromAlgebra i Logika, Vol. 36, No. 5, pp. 483–493, September–October, 1997. 相似文献
15.
Keiji Izuchi 《Journal d'Analyse Mathématique》1998,75(1):135-154
Letb be a Blaschke product with zeros {z
n
} in the open unit disk Δ. Let
be the set of sequences of non-negative integersp=(p
1,p
2,…) such that ∑
n=1
∞
p
n
(1 − |z
n
|) < ∞ andp
n
→∞ asn→∞. We study the class of weak infinite powers ofb,
Properties of these classes depend on the setS(b) of the cluster points in ∂Δ of {z
n
}. It is proved thatS(b)=∂Δ if and only if
, the Douglas algebra generated by
. Also, it is proved thatdθ(S(b))=0 if and only if there exists an interpolating Blaschke productB such that
. 相似文献
16.
李永昆 《应用数学学报(英文版)》1999,15(3):281-286
1.IntroductionNeutraldelayffereatialequationsinpopulationdynamicshavebeenstudiedextensivelyforthep88tfewyears.However,onlyafewpapersll--5]havebeenpublishedontheexistencesofperiodicsolutionsoftheneutraldelaypopulationmodels.In[6,7],Kuangproposedtoinve... 相似文献
17.
Let {S
n
, n=0, 1, 2, …} be a random walk (S
n
being thenth partial sum of a sequence of independent, identically distributed, random variables) with values inE
d
, thed-dimensional integer lattice. Letf
n
=Prob {S
1 ≠ 0, …,S
n
−1 ≠ 0,S
n
=0 |S
0=0}. The random walk is said to be transient if
and strongly transient if
. LetR
n
=cardinality of the set {S
0,S
1, …,S
n
}. It is shown that for a strongly transient random walk with p<1, the distribution of [R
n
−np]/σ √n converges to the normal distribution with mean 0 and variance 1 asn tends to infinity, where σ is an appropriate positive constant. The other main result concerns the “capacity” of {S
0, …,S
n
}. For a finite setA inE
d
, let C(A=Σ
x∈A
) Prob {S
n
∉A, n≧1 |S
0=x} be the capacity ofA. A strong law forC{S
0, …,S
n
} is proved for a transient random walk, and some related questions are also considered.
This research was partially supported by the National Science Foundation. 相似文献
18.
Yusup Kh. Eshkabilov 《Central European Journal of Mathematics》2008,6(1):149-157
Let Ω= [a, b] × [c, d] and T
1, T
2 be partial integral operators in (Ω): (T
1
f)(x, y) =
k
1(x, s, y)f(s, y)ds, (T
2
f)(x, y) =
k
2(x, ts, y)f(t, y)dt where k
1 and k
2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT
1, τ ∈ ℂ and E−τT
2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded operators T
1, T
2, and T = T
1 + T
2 are proved.
相似文献
19.
T. V. Malovichko 《Ukrainian Mathematical Journal》2008,60(11):1789-1802
We consider the solution x
ε of the equation
20.
Let V be a finite dimensional p-adic vector space and let τ be an operator in GL(V). A probability measure μ on V is called τ-decomposable or
if μ = τ(μ)* ρ for some probability measure ρ on V. Moreover, when τ is contracting, if ρ is infinitely divisible, so is μ, and if ρ is embeddable, so is μ. These two subclasses
of
are denoted by L
0(τ) and L
0
#(τ) respectively. When μ is infinitely divisible τ-decomposable for a contracting τ and has no idempotent factors, then it
is τ-semi-selfdecomposable or operator semi-selfdecomposable. In this paper, sequences of decreasing subclasses of the above
mentioned three classes,
, are introduced and several properties and characterizations are studied. The results obtained here are p-adic vector space versions of those given for probability measures on Euclidean spaces. 相似文献
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