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1.
W denotes the category of archimedean ℓ-groups with designated weak unit and ℓ-homomorphisms that preserve the weak unit. Comp denotes the category of compact Hausdorff spaces with continuous maps. The Yosida functor is used to investigate the relationship
between hull classes in W and covering classes in Comp. The central idea is that of a hull class whose hull operator preserves boundedness. We demonstrate how the Yosida functor
may be used to identify hull classes in W and covering classes in Comp. In addition, we exhibit an array of order preserving bijections between certain families of hull classes and all covering
classes, one of which was recently produced by Martínez. Lastly, we apply our results to answer a question of Knox and McGovern
about the class of all feebly projectable ℓ-groups. 相似文献
2.
Ferenc Weisz 《数学学报(英文版)》2010,26(9):1627-1640
A general summability method, the so-called θ-summability is considered for multi-dimensional Fourier transforms. Under some conditions on θ, it is proved that the maximal operator of the θ-means defined in a cone is bounded from the amalgam Hardy space W(hp, e∞) to W(Lp,e∞). This implies the almost everywhere convergence of the θ-means in a cone for all f ∈ W(L1, e∞) velong to L1. 相似文献
3.
We study hypercyclicity and supercyclicity of weighted shifts on ℓ∞, with respect to the weak * topology. We show that there exist bilateral shifts that are weak * hypercyclic but fail to be
weak * sequentially hypercyclic. In the unilateral case, a shift T is weak * hypercyclic if and only if it is weak * sequentially hypercyclic, and this is equivalent to T being either norm, weak, or weak-sequentially hypercyclic on c0 or ℓp (1 ≤ p < ∞). We also show that the set of weak * hypercyclic vectors of any unilateral or bilateral shift on ℓ∞ is norm nowhere dense. Finally, we show that ℓ∞ supports an isometry that is weak * sequentially supercyclic. 相似文献
4.
Nicholas Sparks 《Israel Journal of Mathematics》1998,104(1):125-128
The Banach space ℓ
∞
c
(ω
1) is the space of boundedω
1-sequences of countable support. A pointwise-closed subspaceV≤ℓ
∞
c
(ω
1) will be calledunbounded if lcub;min(supp(υ)):υ ∈Vrcub; is unbounded inω
1. It is shown that there are Lipshitz functionsf: Sph(ℓ
∞
c
(ω
1)) → ℝ which have large variation on the unit sphere of any unbounded subspace. This answers a question implicit in Partington
[P 80]. 相似文献
5.
Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present
a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We prove BIBO
type stability theorems for these systems, both in the discrete and continuous time cases. We also consider the case of dissipative
systems for both discrete and continuous time systems.We further study ℓ
1-ℓ
2 stability in the discrete time case, and L
2-L
∞ stability in the continuous time case. 相似文献
6.
Henk Bruin Juan Rivera-Letelier Weixiao Shen Sebastian van Strien 《Inventiones Mathematicae》2008,172(3):509-533
In this paper, we study the dynamics of a smooth multimodal interval map f with non-flat critical points and all periodic
points hyperbolic repelling. Assuming that |Dfn(f(c))|→∞ as n→∞ holds for all critical points c, we show that f satisfies the so-called backward contracting property with
an arbitrarily large constant, and that f has an invariant probability μ which is absolutely continuous with respect to Lebesgue
measure and the density of μ belongs to Lp for all p<ℓmax/(ℓmax-1), where ℓmax denotes the maximal critical order of f. In the appendix, we prove that various growth conditions on the derivatives along
the critical orbits imply stronger backward contraction. 相似文献
7.
Michel Talagrand 《Israel Journal of Mathematics》1980,37(1-2):181-191
Using the continuum hypothesis, we construct a compact spaceK such that ℓ(K) possesses the Grothendieck property, but such that the unit ball of ℓ(K)′ does not containβ
N, and hence, in particular, such thatl
∞(N) is neither a subspace nor quotient of ℓ(K). In particular,K does not contain a convergent sequence but does not containβ
N.
相似文献
8.
Bui Minh Phong 《Acta Mathematica Hungarica》2006,113(1-2):63-71
Summary We prove that if a complex valued completely multiplicative function F and a positive integer ℓ≦5 satisfy the condition F(N) = Uℓ, where Uℓ is the set of all ℓ-th roots of unity, then {F(n+1) F(n) ∣ nε N} = Uℓ. 相似文献
9.
We give exact criteria for the ℓ-divisibility of the ℓ-regular partition function b
ℓ
(n) for ℓ∈{5,7,11}. These criteria are found using the theory of complex multiplication. In each case the first criterion given corresponds
to the Ramanujan congruence modulo ℓ for the unrestricted partition function, and the second is a condition given by J.-P. Serre for the vanishing of the coefficients
of ∏
m=1∞(1−q
m
)
ℓ−1.
相似文献
10.
Kh. A. Khachatryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(2):94-100
The paper studies a system of nonlinear, vector integro-differential equations with sum and difference kernel and possessing
the trivial solution. A nontrivial solution of the system in the Sobolev spaceW
∞,2×n
(0,+∞) is constructed. 相似文献
11.
W stands for the category of all archimedean l-groups with designated weak unit. The subcategory W
s
of all groups with singular weak unit is analyzed as a full subcategory of W which is both epireflective and monocoreflective. A general technique for "contracting" monoreflections of a category A to a monocoreflective subcategory B is developed and then applied to W
s
to show that: (i) the projectable hull in W
s
is a monoreflection; (ii) essential hulls in W
s
are formed by simply taking the lateral completion, and G is essentially closed in this category if and only if , where X is compact, Hausdorff and extremally disconnected; (iii) the maximum monoreflection on W
s
, denoted , is obtained by contracting the maximum monoreflection on W, and G is epicomplete in W
s
precisely when G is laterally -complete; (iv) the maximum essential reflection on W
s
, denoted , is the contraction of the maximum essential reflection on W.
Received January 22, 1997; accepted in final form June 11, 1998. 相似文献
12.
Ferenc Weisz 《Journal of Fourier Analysis and Applications》2009,15(4):463-487
A general summability method, the so-called θ-summability method is considered for Gabor series. It is proved that if the Fourier transform of θ is in a Herz space then this summation method for the Gabor expansion of f converges to f almost everywhere when f∈L
1 or, more generally, when f∈W(L
1,ℓ
∞) (Wiener amalgam space). Some weak type inequalities for the maximal operator corresponding to the θ-means of the Gabor expansion are obtained. Hardy-Littlewood type maximal functions are introduced and some inequalities are
proved for these. 相似文献
13.
Daniel Pellegrino Eduardo V. Teixeira 《Bulletin of the Brazilian Mathematical Society》2009,40(3):417-431
The main result of the paper shows that, for 1 < p < ∞ and 1 ≤ q < ∞, a linear operator T: ℓ
p
→ ℓ
q
attains its norm if, and only if, there exists a not weakly null maximizing sequence for T (counterexamples can be easily constructed when p = 1). For 1 < p ≠ q < ∞, as a consequence of the previous result we show that any not weakly null maximizing sequence for a norm attaining operator
T: ℓ
p
→ ℓ
q
has a norm-convergent subsequence (and this result is sharp in the sense that it is not valid if p = q). We also investigate lineability of the sets of norm-attaining and non-norm attaining operators. 相似文献
14.
The hardy-littlewood maximal function of a sobolev function 总被引:6,自引:0,他引:6
Juha Kinnunen 《Israel Journal of Mathematics》1997,100(1):117-124
We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW
1,p
(R
n
) for 1<p≤∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal
function of a Sobolev function is quasi-continuous. 相似文献
15.
Romain Tessera 《Monatshefte für Mathematik》2011,61(4):115-118
The Schur algebra is the algebra of operators which are bounded on ℓ
1 and on ℓ
∞. In this note, we exhibit an element of the group algebra of the free group with two generators, which, as a convolution
operator, is invertible in ℓ
2, and whose inverse is not bounded on ℓ
1 nor on ℓ
∞. In particular, this shows that the Schur algebra is not inverse-closed. 相似文献
16.
Ferenc Weisz 《Constructive Approximation》2011,34(3):421-452
A general summability method of more-dimensional Fourier transforms is given with the help of a continuous function θ. Under some weak conditions on θ we show that the maximal operator of the ℓ
1–θ-means of a tempered distribution is bounded from H
p
(ℝ
d
) to L
p
(ℝ
d
) for all d/(d+α)<p≤∞ and, consequently, is of weak type (1,1), where 0<α≤1 depends only on θ. As a consequence we obtain a generalization of the one-dimensional summability result due to Lebesgue, more exactly, the
ℓ
1–θ-means of a function f∈L
1(ℝ
d
) converge a.e. to f. Moreover, we prove that the ℓ
1–θ-means are uniformly bounded on the spaces H
p
(ℝ
d
), and so they converge in norm (d/(d+α)<p<∞). Similar results are shown for conjugate functions. Some special cases of the ℓ
1–θ-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations. 相似文献
17.
Pei-Kee Lin 《数学学报(英文版)》2008,24(5):877-880
We prove that every 2-homogeneous polynomial on the complex co has a unique normpreserving extension to its bidual l∞. 相似文献
18.
It is often observed that interpolation based on translates of radial basis functions or non-radial kernels is numerically
unstable due to exceedingly large condition of the kernel matrix. But if stability is assessed in function space without considering
special bases, this paper proves that kernel-based interpolation is stable. Provided that the data are not too wildly scattered,
the L
2 or L
∞ norms of interpolants can be bounded above by discrete ℓ2 and ℓ ∞ norms of the data. Furthermore, Lagrange basis functions are uniformly bounded and Lebesgue constants grow at most like the
square root of the number of data points. However, this analysis applies only to kernels of limited smoothness. Numerical
examples support our bounds, but also show that the case of infinitely smooth kernels must lead to worse bounds in future
work, while the observed Lebesgue constants for kernels with limited smoothness even seem to be independent of the sample
size and the fill distance. 相似文献
19.
Ozer TALO Feyzi BASAR 《数学学报(英文版)》2008,24(7):1205-1212
Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55(1)(2003), 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp(F) of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp(F) includes the space lp(F) and also shown that the spaces bvp(F) and lp(F) axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given. 相似文献
20.
Krzysztof C. Kiwiel 《Mathematical Programming》2001,90(1):1-25
We study a general subgradient projection method for minimizing a quasiconvex objective subject to a convex set constraint
in a Hilbert space. Our setting is very general: the objective is only upper semicontinuous on its domain, which need not
be open, and various subdifferentials may be used. We extend previous results by proving convergence in objective values and
to the generalized solution set for classical stepsizes t
k
→0, ∑t
k
=∞, and weak or strong convergence of the iterates to a solution for {t
k
}∈ℓ2∖ℓ1 under mild regularity conditions. For bounded constraint sets and suitable stepsizes, the method finds ε-solutions with an
efficiency estimate of O(ε-2), thus being optimal in the sense of Nemirovskii.
Received: October 4, 1998 / Accepted: July 24, 2000?Published online January 17, 2001 相似文献