共查询到20条相似文献,搜索用时 11 毫秒
1.
The present paper is mainly devoted to the study of initial boundary problems associated with a wide class of degenerate second-order differential operators on real intervals, in the framework of weighted continuous function spaces. Such operators are of particular interest, since they often occur, for instance, while building up theoretical models in Mathematical Finance. In order to develop our approach, essentially based on semigroup theory, we provide here some general tools which, perhaps, cover an interest on their own, being concerned with the generation of positive strongly continuous semigroups and their deep connection with Markov processes, in the setting of weighted spaces of continuous functions on a locally compact space. Due to its length, the paper is split up into two parts; the second part will appear in this same journal. 相似文献
2.
This paper is the continuation of [17]. We investigate mapping and spectral properties of pseudodifferential operators of type Ψ with χ χ ? ? and 0 ≤ γ ≤ 1 in the weighted function spaces B (?n, w(x)) and F (?n, w(x)) treated in [17]. Furthermore, we study the distribution of eigenvalues and the behaviour of corresponding root spaces for degenerate pseudodifferential operators preferably of type b2(x) b(x, D) b1(x), where b1(x) and b2(x) are appropriate functions and b(x, D) ? Ψ. Finally, on the basis of the Birman-Schwinger principle, we deal with the “negative spectrum” (bound states) of related symmetric operators in L2. 相似文献
3.
K. Kh. Boimatov 《Journal of Mathematical Sciences》2002,108(4):543-573
Let
W ì \mathbbRn \Omega \subset \mathbb{R}^n
be an open set and l(x)
| u |p,l = ( òW lp (x)| u(x) |p dx )1/p \text (1 \leqslant p < + ¥\text),\left| u \right|_{p,l} = \left( {\int\limits_\Omega {l^p (x)\left| {u(x)} \right|^p dx} } \right)^{1/p} {\text{ (1}} \leqslant p < + \infty {\text{),}} 相似文献
4.
In this paper we study weighted function spaces of type B(?n, Q(x)) and F(?n, Q(x)), where Q(x) is a weight function of at most polynomial growth. Of special interest are the weight functions Q(x) = (1 + |x|2)α/2 with α ? ?. The main result deals with estimates for the entropy numbers of compact embeddings between spaces of this type. 相似文献
5.
6.
Chokri Abdelkefi 《Mediterranean Journal of Mathematics》2012,9(3):499-513
We introduce first weighted function spaces on ${\mathbb{R}^d}$ using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on ${\mathbb{R}^d}$ weighted L p -estimates of the Dunkl transform of a function in terms of an integral modulus of continuity which gives a quantitative form of the Riemann-Lebesgue lemma. Finally, we show in both cases that the Dunkl transform of a function is in L 1 when this function belongs to a suitable Besov-Dunkl space. 相似文献
7.
a∈ C
1([0,1]) vanishing only at 0, 1 and b∈ C ([0,1]), we study existence, qualitative properties, asymptotic behaviour and approximation of the solutions of the degenerate
evolution problem u
t
= (au
z
)
z
- bu in ]0,1[x]0, + ∞[, with u(x,0) = u
0
(x) and boundary conditions a(x)u
x
(x,t) → 0 as x → 0,1, t > 0. 相似文献
8.
Min Zhi ZHAO Hui Zeng ZHANG 《数学学报(英文版)》2007,23(1):111-126
Transience and recurrence are among the most important concepts in Markov processes. In this paper, we study the transience and recurrence for right processes with a given weight function, and characterize them by potentials, excessive functions, first hitting times and last exit times of the process. We also study the properties of recurrent states. 相似文献
9.
10.
This paper focuses on discussing some basic properties of the weighted Markov branching process which is a natural generalisation
of the ordinary Markov branching process. The regularity and uniqueness criteria, which are very easy to verify, are firstly
established. Some important characteristics regarding the hitting times of such structure are obtained. In particular, the
closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the
process is investigated and then the mean explosion time is derived. The mean global holding time and the mean total survival
time are also obtained.
AMS 2000 Subject Classification Primary 60 J27; Secondary 60 J80 相似文献
11.
12.
13.
A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function spaces can be identified as such spaces. We provide a general method to derive Banach frames and atomic decompositions for these Banach spaces by sampling the continuous frame. This is done by generalizing the coorbit space theory developed by Feichtinger and Gröchenig. As an important tool the concept of localization of frames is extended to continuous frames. As a byproduct we give a partial answer to the question raised by Ali, Antoine, and Gazeau whether any continuous frame admits a corresponding discrete realization generated by sampling. 相似文献
14.
15.
16.
We study the boundedness of the HardyLittlewood maximalfunction in weighted Lorentz spaces, using some new techniqueson distribution and rearrangement functions. Our goal is togive a unified version of some well-known weighted inequalitiesin Rn and R+, showing the relation between the theories. 相似文献
17.
We consider the Dirichlet problem for a class of quasilinear degenerate elliptic inclusions of the form ?div(𝒜(x, u, ?u)) + f(x)g(u) ∈ H(x, u, ?u), where 𝒜(x, u, ?u) is allowed to be degenerate. Without the general assumption that the multivalued nonlinearity is characterized by Clarke's generalized gradient of some locally Lipschitz functions, we prove the existence of bounded solutions in weighed Sobolev space with the superlinear growth imposed on the nonlinearity g and the multifunction H(x, u, ?u) by using the Leray-Schauder fixed point theorem. Furthermore, we investigate the existence of extremal solutions and prove that they are dense in the solutions of the original system. Subsequently, a quasilinear degenerate elliptic control problem is considered and the existence theorem based on the proven results is obtained. 相似文献
18.
We develop a general framework to analyze the convergence of linear-programming approximations for Markov control processes in metric spaces. The approximations are based on aggregation and relaxation of constraints, as well as inner approximations of the decision variables. In particular, conditions are given under which the control problems optimal value can be approximated by a sequence of finite-dimensional linear programs. 相似文献
19.
In this paper we study the Cauchy problem for new classes of parabolic type pseudodifferential equations over the rings of finite adeles and adeles. We show that the adelic topology is metrizable and give an explicit metric. We find explicit representations of the fundamental solutions (the heat kernels). These fundamental solutions are transition functions of Markov processes which are adelic analogues of the Archimedean Brownian motion. We show that the Cauchy problems for these equations are well-posed and find explicit representations of the evolution semigroup and formulas for the solutions of homogeneous and non-homogeneous equations. 相似文献
20.
在Banach空间中引进了由有界线性算子引导的广义分布半群的新概念,并讨论了它的有关性质.在我们的方法中,广义分布半群的生成元可以不是稠定的.此外,还引进了退化发展方程在Laplace变换意义下的分布解,应用广义分布半群给出了退化发展方程分布解的构造性表达式. 相似文献