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81.
Antonis Bisbas 《Journal of Mathematical Analysis and Applications》2004,299(2):550-562
A coin-tossing measure μ on [0,1] is a probability measure satisfying
82.
HansTRIEBEL 《数学学报(英文版)》2004,20(4):577-588
The paper deals with multifractal quantities for some types of Radon measures, especially self-similar probability measures, and their relations to Besov spaces. 相似文献
83.
Abstract
In this paper, we establish the relationship between
Hausdorff measures and Bessel capacities on any nilpotent
stratified Lie group
(i. e., Carnot group). In particular, as a special corollary of
our much more general results, we have the following theorem
(see Theorems A and E in Section 1):
Let Q be the
homogeneous dimension of
.
Given any set E ⊂
,
B
α,p
(E) = 0 implies ℋ
Q−αp+ ε(E) = 0 for all ε > 0. On the other
hand, ℋ
Q−αp
(E) < ∞ implies
B
α,p
(E) = 0. Consequently, given any set
E ⊂
of Hausdorff dimension Q −
d, where 0 <
d <
Q, B
α,p
(E) = 0 holds if and only if αp ≤ d.
A version of O. Frostman’s theorem concerning Hausdorff
measures on any homogeneous space is also established using the
dyadic decomposition on such a space (see Theorem 4.4 in Section
4).
Research supported partly by the U. S. National
Science Foundation Grant No. DMS99–70352 相似文献
84.
FengDejun WangYang 《分析论及其应用》2003,19(4):312-331
The Bernoulli convolution Vλ measure is shown to be absolutely continuous with L^2 density for almost all 1/2<λ<1, and singular if λ^-1 is a Pisot number. It is an open question whether the Pisot type Bernoulli conuolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convo-lutions Vλ such that their density functions, if they exist, are not L^2. We also construct other Bernolulli convo-lutions whose density functions if they exist, behave rather badly. 相似文献
85.
A simple method for construction of eigenfunctions of one-electron spin angular momentum operators from products of the primitive one-electron spin functions is presented. Properties of these functions and their applications to the evaluation of some integrals met in theory of quantum similarity are briefly discussed. 相似文献
86.
Ana-Maria Matache Tomáš Roubíček Christoph Schwab 《Advances in Computational Mathematics》2003,19(1-3):73-97
The general theory of approximation of (possibly generalized) Young measures is presented, and concrete cases are investigated. An adjoint-operator approach, combined with quasi-interpolation of test integrands, is systematically used. Applicability is demonstrated on an optimal control problem for an elliptic system, together with one-dimensional illustrative calculations of various options. 相似文献
87.
Nikita Szidorov 《Acta Mathematica Hungarica》2003,98(4):345-355
The aim of this paper is to prove some fixed point theorems which generalize well known basic fixed point principles of nonlinear
functional analysis. Moreover, we investigate the class of mappings f: X→ X, where X is a Banach space, for which one of the main conditions in the metric fixed point theory, namely the condition (1), is satisfied.
We obtain essential applications of this fact. All our results are illustrated by suitable examples.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
88.
Fulvio Ricci Giancarlo Travaglini 《Proceedings of the American Mathematical Society》2001,129(6):1739-1744
Let be a convex curve in the plane and let be the arc-length measure of Let us rotate by an angle and let be the corresponding measure. Let . Then This is optimal for an arbitrary . Depending on the curvature of , this estimate can be improved by introducing mixed-norm estimates of the form where and are conjugate exponents. 相似文献
89.
Zvi Artstein 《Set-Valued Analysis》2001,9(1-2):13-34
The paper establishes the continuity of the best approximation, or the projection, of a function in L
p
for p[1,), on a closed convex set in the space, when the set varies and converges to a limit set in the Young-measure relaxation of the space. To this end a strong-type convergence and a convexity structure are identified on the space of Young measures. The appropriate convergence of sets with respect to which the continuity holds is the Mosco convergence of sets associated with the strong-type convergence of functions. 相似文献
90.
A multiresolution analysis is defined in a class of locally compact abelian groups G. It is shown that the spaces of integrable functions
and the complex Radon measures M(G) admit a simple characterization in terms of this multiresolution analysis. 相似文献