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1.
2.
Let Γ be the set of all permutations of the natural series and let α = {α j}
j∈ℕ, ν = {νj}
j∈ℕ, and η = {ηj}
j∈ℕ be nonnegative number sequences for which
is defined for all γ:= {γ(j)}
j∈ℕ ∈ Γ and η ∈ l
p. We find
in the case where 1 < p < ∞.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1430–1434, October, 2005. 相似文献
3.
For two complex Banach spaces X and Y,
(B
X; Y) will denote the space of bounded and continuous functions from B
X
to Y that are holomorphic on the open unit ball. The numerical radius of an element h in
(B
X; X) is the supremum of the set
. We prove that every complex Banach space X with the Radon-Nikodym property satisfies that the subset of numerical radius attaining functions in
(B
X; X) is dense in
(B
X; X). We also show the denseness of the numerical radius attaining elements of
in the whole space, where
is the subset of functions in
which are uniformly continuous on the unit ball. For C(K) we prove a denseness result for the subset of the functions in
(B
C(K); C(K)) which are weakly uniformly continuous on the closed unit ball. For a certain sequence space X, there is a 2-homogenous polynomial P from X to X such that for every R > e, P cannot be approximated by bounded and numerical radius attaining holomorphic functions defined on RB
X
. If Y satisfies some isometric conditions and X is such that the subset of norm attaining functions of
(B
X; ℂ) is dense in
(B
X; ℂ), then the subset of norm attaining functions in
(B
X; Y) is dense in the whole space.
The first author was supported in part by D.G.E.S. Project BFM2003-01681.
The second author’s work was performed during a visit to the Departamento de Análisis Matem’atico of Universidad de Granada,
with a grant supported by the Korea Research Foundation under grant (KRF-2002-070-C00006). 相似文献
4.
M. Rudelson 《Israel Journal of Mathematics》1999,111(1):143-155
Lett≥1 and letn, M be natural numbers,n<M. Leta=(a
i,j
) be ann xM matrix whose rows are orthonormal. Suppose that the ℓ2-norms of the columns ofA are uniformly bounded. Namely, for allj
Using majorizing measure estimates we prove that for every ε>0 there exists, a setI ⊃ {1,…,M} of cardinality at most
such that the matrix
, whereA
I
=(a
i,j
)
j∈I
, acts as a (1+ε)-isomorphism from ℓ
2
n
into
.
Research supported in part by a grant of the US-Israel BSF. Part of this research was performed when the author held a postdoctoral
position at MSRI. Research at MSRI was supported in part by NSF grant DMS-9022140. 相似文献
5.
We exhibit, for any integerg≥2, an infinite sequenceA ∈B
2[g] such that
. Furthermore, we obtain better estimates for small values ofg. For instance, we exhibit an infinite sequenceA ∈B
2[2] such that
Partially supported by Colciencias, Colombia and Universidad del Cauca. 相似文献
6.
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
7.
Jin-hong You Gemai Chen Min Chen Xue-lei JiangUniversity of Regina Regina Saskatchewan SS OA CanadaUniversity of Calgary Calgary Alberta TN N CanadaAcademy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2003,19(3):363-370
Consider the partly linear regression model ,where yi's are responses, xi = (xi1, xi2,…,xip)' and ti ∈T are known and nonrandom design points, T is a compact set in the real line is an unknown parameter vector, g(·) is an unknown function and {Ei} isa linear process, i.e., random variables with zeromean and variance o2e. Drawing upon B-spline estimation of g(·) and least squares estimation of 0, we construct estimators of the autocovariances of {Ei}- The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {Ei} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coefficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process. 相似文献
8.
We prove a local variational principle of pressure for any given open cover. More precisely, for a given dynamical system
(X, T), an open cover
of X, and a continuous, real-valued function f on X, we show that the corresponding local pressure P(T, f;
) satisfies
, moreover, the supremum can be attained by a T-invariant ergodic measure. By establishing the upper semi-continuity and affinity of the entropy map relative to an open
cover, we further show that
for any T-invariant measure μ of (X, T), i.e., local pressures determine local measure-theoretic entropies. As applications, properties of both local and global
equilibrium states for a continuous, real-valued function are studied.
The first author is partially supported by NSFC Grants 10531010 and 10401031, program of new century excellent talents in
universities, special foundation on excellent Ph.D thesis, and presidential award of the Chinese Academy of Sciences.
The second author is partially supported by NSF grant DMS0204119 and NSFC grant 10428101. 相似文献
9.
E.M.E.ZAYED 《数学学报(英文版)》2004,20(2):209-222
The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. 相似文献
10.
Michael Lin 《Israel Journal of Mathematics》1970,8(4):357-366
LetP be a conservative and ergodic Markov operator onL
1(X, Σ,m). We give a sufficient condition for the existence of a decompositionA
f
↑X such that for 0≦f, g ∈L
∞ (A
j
) and any two probability measuresμ andν weaker thanm
, whereλ is theσ-finite invariant measure (which necessarily exists). Processes recurrent in the sense of Harris are shown to have this decomposition,
and an analytic proof of the convergence of
is deduced for such processes.
This paper is a part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the direction of Professor
S. R. Foguel, to whom the author is grateful for his helpful advice and kind encouragement. 相似文献
11.
Xi Mei WU Qin YUE 《数学学报(英文版)》2007,23(11):2061-2068
Let F = Q(√-p1p2) be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol (p1/p2) = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold: (1) The quartic residue symbols (p1/p2)4 = (p2/p1)4 = 1; (2) Either both
p1 and p2 are represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=ε(2x^2-p1y^2),x,y∈Z,ε∈{±1},where h+(2p1) is the narrow class number of Q(√2p1),Moreover, we also generalize these results. 相似文献
12.
Peter Šemrl 《Israel Journal of Mathematics》2008,163(1):125-138
Let
be an arbitrary division ring and M
n
(
) the multiplicative semigroup of all n × n matrices over
. We describe the general form of endomorphisms of M
n
(
).
Supported in part by a grant from the Ministry of Science of Slovenia. 相似文献
13.
Abstract This paper computes the Thom map on γ2 and proves that it is represented by 2b2,0h1,2 in the ASS. The authors also compute the higher May differential of b2,0, from which it is proved that
for 2 ≤ s < p - 1 are permanent cycles in the ASS.
* Project supported by the National Natural Science Foundation of China (No.10501045), the Tianyuan Foundation of Mathematics
(No.10426028) and the Fund of the Personnel Division of Nankai University. 相似文献
14.
E. M. E. ZAYED 《数学学报(英文版)》2005,21(4):733-752
The trace of the wave kernel μ(t) =∑ω=1^∞ exp(-itEω^1/2), where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 (δ/δxk)^2 in the (x^1, x^2, x^3)-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ (t) on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j (j = 1,……, n), where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^* (i = 1 + kj-1,……, kj) of the bounding surfaces S j are considered, such that S j = Ui-1+kj-1^kj Si^*, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω (e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature) are determined from the asymptotic expansion ofexpansion of μ(t) for small │t│. 相似文献
15.
Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(4):611-622
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation
相似文献
16.
I. E. Chyzhykov 《Ukrainian Mathematical Journal》2007,59(7):1088-1109
For arbitrary 0 ≤ σ ≤ ρ ≤ σ + 1, we describe the class A
σ
ρ
of functions g(z) analytic in the unit disk
= {z : ∣z∣ < 1} and such that g(z) ≠ 0, ρT[g] = σ, and ρM[g] = ρ, where
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 979–995, July, 2007. 相似文献
17.
Frank Blume 《Israel Journal of Mathematics》1998,108(1):1-12
If (X,T) is a completely ergodic system, then there exists a positive monotone increasing sequence {a
n
}
n
1/∞
with lim
n
→∞a
n
=∞ and a positive concave functiong defined on [1, ∞) for whichg(x)/x
2 isnot integrable such that
for all nontrivial partitions α ofX into two sets. 相似文献
18.
R. Nair 《Israel Journal of Mathematics》2009,171(1):197-219
We consider a system of “generalised linear forms” defined at a point x = (x
(i, j)) in a subset of R
d
by
for k ≥ 1. Here d = d
1 + ⋯ + d
l
and for each pair of integers (i, j) ∈ D, where D = {(i, j): 1 ≤ i ≤ l, 1 ≤ j ≤ d
i
} the sequence of functions (g
(i, j), k
(x))
k=1∞ are differentiable on an interval X
ij
contained in R. We study the distribution of the sequence on the l-torus defined by the fractional parts X
k
(x) = ({ L
1(x)(k)}, ..., {L
l
(x)(k)}) ∈ T
l
, for typical x in the Cartesian product . More precisely, let R = I
1 × ⋯ × I
l
be a rectangle in T
l
and for each N ≥ 1 define a pair correlation function
and a discrepancy , where the supremum is over all rectangles in T
l
and χ
R
is the characteristic function of the set R. We give conditions on (g
(i, j), k
(x))
k=1∞ to ensure that given ε > 0, for almost every x ∈ T
l
we have Δ
N
(x) = o(N(log N)
l+∈). Under related conditions on(g
(i, j), k
(x))
k =1∞ we calculate for appropriate β ∈ (0, 1) the Hausdorff dimension of the set {x : lim sup
N→∞
N
β Δ
N
(x > 0)}. Our results complement those of Rudnick and Sarnak and Berkes, Philipp, and Tichy in one dimension and M. Pollicott
and the author in higher dimensions. 相似文献
19.
Xiao Hong CAO Mao Zheng GUO Bin MENG 《数学学报(英文版)》2006,22(1):169-178
When A ∈ B(H) and B ∈ B(K) are given, we denote by Mc an operator acting on the Hilbert space HΘ K of the form Me = ( A0 CB). In this paper, first we give the necessary and sufficient condition for Mc to be an upper semi-Fredholm (lower semi-Fredholm, or Fredholm) operator for some C ∈B(K,H). In addition, let σSF+(A) = {λ ∈ C : A-λI is not an upper semi-Fredholm operator} bc the upper semi-Fredholm spectrum of A ∈ B(H) and let σrsF- (A) = {λ∈ C : A-λI is not a lower semi-Fredholm operator} be the lower semi Fredholm spectrum of A. We show that the passage from σSF±(A) U σSF±(B) to σSF±(Mc) is accomplished by removing certain open subsets of σSF-(A) ∩σSF+ (B) from the former, that is, there is an equality σSF±(A) ∪σSF± (B) = σSF± (Mc) ∪& where L is the union of certain of the holes in σSF±(Mc) which ilappen to be subsets of σSF- (A) A σSF+ (B). Weyl's theorem and Browder's theorem are liable to fail for 2 × 2 operator matrices. In this paper, we also explore how Weyl's theorem, Browder's theorem, a-Weyl's theorem and a-Browder's theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space. 相似文献
20.
E. M. E. Zayed 《数学学报(英文版)》2000,16(4):627-636
Abstract
Small-time asymptotics of the trace of the heat semigroup
where {μ
ν
} are the eigenvalues of the negative Laplacian
in the (x
1, x
2)-plane, is studied for a general bunded domain Ω with a smooth boundary ∂Ω, where a finite number of Dirichlet, Neumann and
Robin boundary conditions, on the piecewise smooth parts Γ
i
(i = 1, ..., n) of ∂Ω such that
, are considered. Some geometrical properties associated with Ω are determined. 相似文献