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1.
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
2.
In this note we are interested in the graded modulesM
k=I(k)/Ik and
, whereI is a saturated ideal in the homogeneous coordinate ringS=K[x0,…,xn] of ℙn,I
(k) is the symbolic power and
is the saturation of the ordinary power. Very little is known about these modules, and we provide a bound on their diameters,
we compute the Hilbert functions and we study some characteristic submodules in the special case ofn+1 general points in ℙn.
Sunto In questa nota siamo interessati ai moduli graduatiM k=I(k)/Ik e , doveI è un ideale saturato nell'anello delle coordinate omogeneeS:=K[x0,…,xn] di ℙn,I (k) è la potenza simbolica e è la saturazione della potenza ordinaria. Poco è noto su questi moduli e qui viene fornito un limite superiore ai loro diametri. Ne calcoliamo inoltre le funzioni di Hilbert e studiamo alcuni sottomoduli caratteristici nel caso speciale din+1 punti in posizione generale, in ℙn.相似文献
3.
Let {zk=xk+iyk} be a sequence on upper half plane
and {si} be the number of appearence of zk in {z1,z2,...,zk}. Suppose sup si<+∞. Let ω(x) be a weight belonging to A∞ and
. We Consider the weighted Hardy space
and operator Tp mapping f(z)∈H
+w
p
into a sequence defined by
, 0<p≤+∞, j=1,2,.... Then Tp(H
+w
p
)=lp if and only if {zk} is uniformly separated. Besides the effective solution for interpolation is obtained.
Supported by National Science Foundation of China and Shanghai Youth Science Foundation 相似文献
4.
Katsunori Iwasaki 《Journal d'Analyse Mathématique》1997,72(1):279-298
LetP be ann-dimensional regular simplex in ℝn centered at the origin, and let P(k) be thek-skeleton ofP fork = 0, 1,…,n. Then the set
of all continuous functions in ℝn satisfying the mean value property with respect to P(k) forms a finite-dimensional linear space of harmonic polynomials. In this paper the function space
is explicitly determined by group theoretic and combinatorial arguments for symmetric polynomials. 相似文献
5.
We investigate the correlation between the constants K(ℝn) and
, where
is the exact constant in a Kolmogorov-type inequality, ℝ is the real straight line,
, L
l
p, p
(G
n) is the set of functions ƒ ∈ L
p
(G
n
) such that the partial derivative
belongs to L
p
(G
n
),
, 1 ≤ p ≤ ∞, l ∈ ℕn, α ∈ ℕ
0
n
= (ℕ ∪ 〈0〉)n, D
α
f is the mixed derivative of a function ƒ, 0 < μi < 1,
, and ∑
i=0
n
. If G
n
= ℝ, then μ0=1−∑
i=0
n
(α
i
/l
i
), μi = αi/l
i
,
if
, then μ0=1−∑
i=0
n
(α
i
/l
i
) − ∑
i=0
n
(λ/l
i
), μi = αi/ l
i
+ λ/l
i
,
, λ ≥ 0. We prove that, for λ = 0, the equality
is true.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 597–606, May, 2006. 相似文献
6.
Henry Teicher 《Journal of Theoretical Probability》1995,8(4):779-793
Conditions are obtained for (*)E|S
T
|γ<∞, γ>2 whereT is a stopping time and {S
n=∑
1
n
,X
j
ℱ
n
,n⩾1} is a martingale and these ensure when (**)X
n
,n≥1 are independent, mean zero random variables that (*) holds wheneverET
γ/2<∞, sup
n≥1
E|X
n
|γ<∞. This, in turn, is applied to obtain conditions for the validity ofE|S
k,T
|γ<∞ and of the second moment equationES
k,T
2
=σ
2
EΣ
j=k
T
S
k−1,j−1
2
where
and {X
n
, n≥1} satisfies (**) and
,n≥1. The latter is utilized to elicit information about a moment of a stopping rule. It is also shown for i.i.d. {X
n
, n≥1} withEX=0,EX
2=1 that the a.s. limit set of {(n log logn)−k/2
S
k,n
,n≥k} is [0,2
k/2/k!] or [−2
k/2/k!] according ask is even or odd and this can readily be reformulated in terms of the corresponding (degenerate kernel)U-statistic
. 相似文献
7.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
8.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
9.
Ian M. Wanless 《Combinatorica》2006,26(6):743-745
Let
denote the set of n×n binary matrices which have each row and column sum equal to k. For 2≤k≤n→∞ we show that
is asymptotically equal to (k−1)k−1k2−k. This confirms Conjecture 23 in Minc's catalogue of open problems.
* Written while the author was employed by the Department of Computer Science at the Australian National University. 相似文献
10.
Consider the parameter space Θ which is an open subset of ℝ
k
,k≧1, and for each θ∈Θ, let the r.v.′sY
n
,n=0, 1, ... be defined on the probability space (X,A,P
θ) and take values in a Borel setS of a Euclidean space. It is assumed that the process {Y
n
},n≧0, is Markovian satisfying certain suitable regularity conditions. For eachn≧1, let υ
n
be a stopping time defined on this process and have some desirable properties. For 0 < τ
n
→ ∞ asn→∞, set
h
n
→h ∈R
k
, and consider the log-likelihood function
of the probability measure
with respect to the probability measure
. Here
is the restriction ofP
θ to the σ-field induced by the r.v.′sY
0,Y
1, ...,
. The main purpose of this paper is to obtain an asymptotic expansion of
in the probability sense. The asymptotic distribution of
, as well as that of another r.v. closely related to it, is obtained under both
and
.
This research was supported by the National Science Foundation, Grant MCS77-09574.
Research supported by the National Science Foundation, Grant MCS76-11620. 相似文献
11.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
12.
W. Luh T. Meyrath M. Niess 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(6):365-371
The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ n } ? ?, there exists a function ?, meromorphic on ?, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n k } of ? such that $ \left\{ {\varphi \left( {z + \lambda _{n_k } } \right)} \right\} The paper proves the following result on universal meromorphic approximation: Given any unbounded sequence {λ
n
} ⊂ ℂ, there exists a function ϕ, meromorphic on ℂ, with the following property. For every compact set K of rational approximation (i.e. Vitushkin set), and every function f, continuous on K and holomorphic in the interior of K, there exists a subsequence {n
k
} of ℕ such that
converges to f(z) uniformly on K.
A similar result is obtained for arbitrary domains G ≠ ℂ. Moreover, in case {λ
n
}={n} the function ϕ is frequently universal in terms of Bayart/Grivaux [3].
Original Russian Text ? W.Luh, T.Meyrath, M.Niess, 2008, published in Izvestiya NAN Armenii. Matematika, 2008, No. 6, pp.
66–75. 相似文献
13.
By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the
asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation
, on a time scale . The results improve some oscillation results for neutral delay dynamic equations and in the special case when = ℝ our results cover and improve the oscillation results for second-order neutral delay differential equations established
by Li and Liu [Canad. J. Math., 48 (1996), 871–886]. When = ℕ, our results cover and improve the oscillation results for second order neutral delay difference equations established
by Li and Yeh [Comp. Math. Appl., 36 (1998), 123–132]. When =hℕ, = {t: t = q
k
, k ∈ ℕ, q > 1}, = ℕ2 = {t
2: t ∈ ℕ}, = = {t
n
= Σ
k=1
n
, n ∈ ℕ0}, ={t
2: t ∈ ℕ}, = {√n: n ∈ ℕ0} and ={: n ∈ ℕ0} our results are essentially new. Some examples illustrating our main results are given.
相似文献
14.
H. Teicher 《Probability Theory and Related Fields》1988,79(2):303-316
Summary If
where {X
n j
,ℱ
n j
1≦j≦m
n
↑∞, n≧1} is a martingale difference array, conditions are given for the distribution and moment convergence of S
n,k
to the distribution and moments of
where H
k
is the Hermite polynomial of degree k and Z is a standard normal variable. This is intimately related to an identity (*) for multiple Wiener integrals. Under alternative
conditions, similar results hold for S
n, k
/U
n
k
and S
n, k
/V
n
k
where
and V
n
2
V
n
2
is the conditional variance.
Research supported by the National Science Foundation under Grant DMS-8601346 相似文献
15.
An (n,k)-affine source over a finite field is a random variable X = (X
1,..., X
n
) ∈ , which is uniformly distributed over an (unknown) k-dimensional affine subspace of . We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger
than n
c
(where c is a large enough constant). Our main results are as follows:
Research supported by Israel Science Foundation (ISF) grant. 相似文献
1. | (For arbitrary k): For any n,k and any of size larger than n 20, we give an explicit construction for a function D : → , such that for any (n,k)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. |
2. | (For k=1): For any n and any of size larger than n c , we give an explicit construction for a function D: , such that for any (n, 1)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. Here, δ>0 is an arbitrary small constant, and c is a constant depending on δ. |
16.
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
17.
Saharon Shelah 《Israel Journal of Mathematics》2008,166(1):61-96
We show that, consistently, there is an ultrafilter on ω such that if N
nℓ = (P
nℓ ∪ Q
nℓ, P
nℓ, Q
nℓ, R
nℓ) (for ℓ = 1, 2, n < ω), P
nℓ ∪ Q
nℓ ⊆ ω, and are models of the canonical theory t
ind of the strong independence property, then every isomorphism from onto is a product isomorphism.
The first version of this work done in 93; First typed: May 1993.
This research was partially supported by the United States-Israel Binational Science Foundation. Publication 509 相似文献
18.
Yu Cheng Li 《数学学报(英文版)》2008,24(10):1737-1750
In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z^ng(z) (n ≥1), g(z) = b0 + b1z^p1 +b2z^p2 +.. , bk ≠ 0 (k = 0, 1, 2,...), our main result is =A′(Mf) = A′(Mzn)∩A′(Mg) = A′(Mz^s), where s = g.c.d.(n,p1,p2,...). In the last section, we study the relation between strongly irreducible curve and the winding number W(f,f(α)), α ∈ D. 相似文献
19.
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
20.
Marian Genčev 《Mathematica Slovaca》2009,59(3):365-378
The aim of the paper is the investigation of special infinite series of the form
where (a, b, m
1, m
2, θ, c, P(n)) ∈ ℝ4 × ℂ × {±1} ×
[n] and is a sequence of rational functions. A general summation method for the sum above in the case of the special choice of parameters
a, b and f
n
(n) is included. We find the 2m-tuple of rational numbers α
i
, β
j
(1 ≤ i ≤ m, 1 ≤ j ≤ m) for which
iff
and vice versa.
相似文献