共查询到20条相似文献,搜索用时 15 毫秒
1.
Using Hankel transform the symbol 'a' is defined and the pseudo-differential operator (p.d.o.) hμ,a associated with the Bessel operator d 2/dx 2 + (1 ? 4μ 2)/4x 2 in terms of this symbol is defined. It is shown that the operator hμ,a is a continuous linear map of a Hankel invariant space into itself. A special pseudo-differential operator called the Hankel potential is defined and some of its properties are investigated. 相似文献
2.
Some Processes Associated with Fractional Bessel Processes 总被引:1,自引:0,他引:1
Let
be a d-dimensional fractional Brownian motion with Hurst parameter H and let
be the fractional Bessel process. Itôs formula for the fractional Brownian motion leads to the equation
. In the Brownian motion case
is a Brownian motion. In this paper it is shown that Xt is not an
-fractional Brownian motion if H 1/2. We will study some other properties of this stochastic process as well. 相似文献
3.
4.
We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann
transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space.
Received: May 11, 2007. Revised: May 20, 2008. Accepted: May 23, 2008. 相似文献
5.
Jorge J. Betancor Juan C. Fariña Lourdes Rodríguez-Mesa Alejandro Sanabria-García 《Journal of Fourier Analysis and Applications》2008,14(4):493-513
In this paper we establish transference results showing that the boundedness of the conjugate operator associated with Hankel
transforms on Lorentz spaces can be deduced from the corresponding boundedness of the conjugate operators defined on Laguerre,
Jacobi, and Fourier–Bessel settings. Our result also allows us to characterize the power weights in order that conjugation
associated with Laguerre, Jacobi, and Fourier–Bessel expansions define bounded operators between the corresponding weighted
L
p
spaces.
This paper is partially supported by MTM2004/05878. Third and fourth authors are also partially supported by grant PI042004/067. 相似文献
6.
Liu Lanzhe 《东北数学》1997,(1)
BoundednesofSingularIntegralOperatorsOnSomeAtomSpacesLiuLanzhe(刘岚吉吉)(DepartmentofAppliedMathematics,HunanUniversity,Changsha,... 相似文献
7.
On the Sobolev boundedness results of the product of pseudo-differential operators involving a couple of fractional Hankel transforms
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This article is concerned with the study of pseudo-differential operators associated with fractional Hankel transform. The product of two fractional pseudo-differential operators is defined and investigated its basic properties on some function space. It is shown that the pseudo-differential operators and their products are bounded in Sobolev type spaces. Particular cases are discussed. 相似文献
8.
希氏空间中算子样条插值及算子方程的近似解 总被引:2,自引:0,他引:2
本文首先讨论希氏空间中由有界线性算子T确定的抽象插值样条(本文称T样条)的构造,通过引入新的内积得到T样条的投影特征和表达式.然后研究算子方程Tx=y的投影近似解和T样条近似解,并给出了两种近似解误差之间的关系. 相似文献
9.
Andrzej Dabrowski 《Journal of Combinatorial Theory, Series A》1997,80(2):385-544
We give short elementary proof of some combinatorial result in the theory of automorphic pseudodifferential operators. 相似文献
10.
We study a 22 operator matrix associated with a closed densely
defined operator. Among others, the selfadjointness of a closed symmetric
operator and the strong commutativity of two (unbounded) self-adjoint operators
are characterized in terms of the related operator matrices. We propose
a definition of strong commutativity for closed symmetric operators.
Submitted: November 8, 2001 相似文献
11.
Continuity is obtained of some multilinear operators related to certain integral operators for the weighted Herz spaces with extreme exponents. The operators include the Littlewood–Paley and Marcinkiewicz operators. 相似文献
12.
The operator equation λM_zX = XM_(zk), for k ≥ 2, λ∈ C, is completely solved.Further, some algebraic and spectral properties of the solutions of the equation are discussed. 相似文献
13.
J. J. Betancor B. J. Gonzá lez 《Proceedings of the American Mathematical Society》2001,129(1):219-228
In this paper we introduce new function spaces that are denoted by , -1/2$"> and and that are spaces of type where the Hankel convolution and the Hankel transformation are defined. The spaces will play the same role in the Hankel setting that the spaces play in the theory of Fourier transformation. 相似文献
14.
S. K. Upadhyay 《Applicable analysis》2013,92(4):415-428
Lp-norm type inequalities for pseudo-differential operators L(x,D) and H(x,D) are derived for 1 ≤ p < ∞. Product of pseudo-differential operators associated with Bessel operator Sμ are defined and its Lp-norm type inequalities are obtained. 相似文献
15.
借鉴Orlicz-Sobolev空间中的受控最佳逼近算子问题的研究结果,抓住Musielak-Orlicz-Sobolev空间的构成特点,利用△_2条件及其否定,给出了MusielakOrlicz-Sobolev空间具有序连续性的充要条件,同时研究了该空间中最佳逼近算子的连续性. 相似文献
16.
Christoph Dorschfeldt Bert-Wolfgang Schulze 《Annals of Global Analysis and Geometry》1994,12(1):135-171
The pseudo-differential Mellin-edge-approach is a tool for studying differential and pseudo-differential operators on manifolds with corners. The Mellin transform, acting on the corner axis +, is a substitute for the Fourier transform along edge variables in the calculus of wedge pseudo-differential operators. The basic elements of that theory (cf. Schulze [6,8]) are extended to edges like +
t with a control of symbols and smoothing operators near the vertext=0. The authors study the weighted Mellin wedge Sobolev spaces, the operator-valued Mellin convention translating Fourier symbols into Mellin ones under preserved smoothness up tot=0, and develop an operator calculus with its characterization on the level of symbols. Throughout the theory, there are involved one-parameter groups of isomorphisms acting on the Banach spaces that are the abstract analogues of the weighted cone Sobolev spaces. 相似文献
17.
高进寿 《数学物理学报(A辑)》2000,20(1):41-47
在文中,对于C^m中有界强拟凸域Ω,得到了Bergman空间A^2(Ω)上的Hankel算子Hf(f∈L^2(Ω,dv)的本性范数∥Hf∥ess(在L^2(Ω,dv上)的等价刻划。 相似文献
18.
We obtain sufficient conditions for the continuity of the general nonlinear superposition operator (generalized Nemytskii operator) acting from the space
of differentiable functions on a bounded domain
to the Lebesgue space
. The values of operators on a function
are locally determined by the values of both the function
itself and all of its partial derivatives up to order
inclusive. In certain particular cases, the sufficient conditions obtained are proved to be necessary as well. The results are illustrated by several examples, and an application to the theory of Sobolev spaces is also given. 相似文献
19.
A new result for integrals involving the product of Bessel functions and Associated Laguerre polynomials is obtained in terms
of the hypergeometric function. Some special cases of the general integral lead to interesting finite and infinite series
representations of hypergeometric functions. 相似文献