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61.
62.
Clyde D Hardin 《Journal of multivariate analysis》1982,12(3):385-401
The so-called spectral representation theorem for stable processes linearly imbeds each symmetric stable process of index p into Lp (0 < p ≤ 2). We use the theory of Lp isometries for 0 < p < 2 to study the uniqueness of this representation for the non-Gaussian stable processes. We also determine the form of this representation for stationary processes and for substable processes. Complex stable processes are defined, and a complex version of the spectral representation theorem is proved. As a corollary to the complex theory we exhibit an imbedding of complex Lq into real or complex Lp for 0 < p < q ≤ 2. 相似文献
63.
G. R. Bates 《Journal of Optimization Theory and Applications》1978,24(4):639-649
Lower closure theorems are proved for optimal control problems governed by ordinary differential equations for which the interval of definition may be unbounded. One theorem assumes that Cesari's property (Q) holds. Two theorems are proved which do not require property (Q), but assume either a generalized Lipschitz condition or a bound on the controls in an appropriateL
p-space. An example shows that these hypotheses can hold without property (Q) holding. 相似文献
64.
The purpose of the present note is to provide a somewhat more flexible statement of the sufficiency conditions in Section 4 of Ref. 1 and to give explicit statements of the fundamental necessity and sufficiency results, which were only implicitly presented there. The additional flexibility is obtained by considering local, rather than global, pseudoconcavity requirements. 相似文献
65.
This paper is concerned with large- error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales. 相似文献
66.
WeiJieFENG 《数学学报(英文版)》2004,20(6):983-988
In this paper, we obtain some existence results for a class of singular semilinear elliptic problems where we improve some earlier results of Zhijun Zhang. We show the existence of entire positive solutions without the monotonic condition imposed in Zhang‘s paper. The main point of our technique is to choose an approximating sequence and prove its convergence. The desired compactness can be obtained by the Sobolev embedding theorems. 相似文献
67.
C.?BacutaEmail author J. H.?Bramble 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):874-878
The Dirichlet problem for the plane elasticity problem
on a convex polygonal domain is considered and it is proved that
for data in
L
2
the
H
2
regularity estimate holds with
constants independent of the Lamé coefficients. 相似文献
68.
Ravi P. Agarwal Said R. Grace Donal O'Regan 《Proceedings of the American Mathematical Society》2003,131(1):129-140
This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.
69.
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
70.
GuangGuiDING 《数学学报(英文版)》2003,19(4):793-800
In this paper,we study the extension of isometries between the unit spheres of some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S1(E) of all smooth points of the unit sphere S1(E) is dense in S1(E),then under some condition,every surjective isometry V0 from S1(E) onto S1(C(Ω)) can be extended to be a real linearly isometric map V of E onto C(Ω).From this resultwe also obtain some corollaries. This is the first time we study this problem on different typical spaces,and the method of proof is also very different too. 相似文献