共查询到19条相似文献,搜索用时 93 毫秒
1.
2.
利用Bloch型空间中函数的导数的估计,通过构造一些新的检验函数,运用解析函数的性质与算子理论,给出了不同Bloch型空间中的积型算子紧性的特征. 相似文献
3.
卢克平 《数学年刊A辑(中文版)》1990,(5)
本文包含两部分内容。第一部分,讨论了超球上的Bloch函数和小Bloeh函数。并把S.Axlor关于单复变数Bloch函数和小Bloeh函数的特征分别推广到C~n中。第二部分证明了:1.Hankel算子H-_f为有界线性算子的充要条件是f为Bloch函数,2.H-_f为紧算子的充要条件是f为小Bloch函数。 相似文献
4.
5.
《数学年刊A辑(中文版)》2005,(1)
Clifford分析中的Hilbert一Dirae算子 F .BRACKX H.De SCHEPPER 围绕LaPlace算子的“平方根”这一中心主题,证明了第一类和第二类的古典Riesz位势依然适于结合涉及Dirac算子的自然的和复数幂的所谓Hllbert一Dirac卷积算子的显式表示. ETA不变t、微分特征及平坦向t丛 J .h度.BIS 相似文献
6.
本文研究了Bloch函数空间上紧乘积算子,引入了消失α-Caleson测度,利用它给出Bloch空间和小Bloch空间上的乘积算子Mφf=φf紧性的一个充分条件。 相似文献
7.
本文研究了非自伴Dirac算子的一般两点边值问题的渐近迹,首先运用平移算子得到了其Cauchy问题解的渐近式,并由此及边界条件,构造了整函数ω(λ),利用它将边界条件分为八种基本类型,最后采用留数的方法,得到了四种主要类型的特征值的渐近迹公式。 相似文献
8.
利用泛函分析多复变方法.研究了多圆柱上Bloch空间的加权复合算子的一些性质.并且通过圆柱的全纯自映射φ及全纯函数ψ的一些特性.分别给出了多圆柱上Bloch空间上由φ及ψ确定的加权复合算子的有界性与紧性的充要条件. 相似文献
9.
10.
11.
Ricardo Abreu-Blaya Juan Bory-Reyes Fred Brackx Hennie De Schepper Frank Sommen 《Complex Analysis and Operator Theory》2012,6(5):971-985
The theory of complex Hermitean Clifford analysis was developed recently as a refinement of Euclidean Clifford analysis; it focusses on the simultaneous null solutions, called Hermitean monogenic functions, of two Hermitean Dirac operators constituting a splitting of the traditional Dirac operator. In this function theory, the fundamental integral representation formulae, such as the Borel?CPompeiu and the Clifford?CCauchy formula have been obtained by using a (2 ×?2) circulant matrix formulation. In the meantime, the basic setting has been established for so-called quaternionic Hermitean Clifford analysis, a theory centred around the simultaneous null solutions, called q-Hermitean monogenic functions, of four Hermitean Dirac operators in a quaternionic Clifford algebra setting. In this paper we address the problem of establishing a quaternionic Hermitean Clifford?CCauchy integral formula, by following a (4?× 4) circulant matrix approach. 相似文献
12.
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called Dirac operator, which factorizes the Laplacian; monogenic functions may thus also be seen as a generalization of holomorphic functions in the complex plane. Hermitian Clifford analysis offers yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitian (or h-) monogenic functions, of two Hermitian Dirac operators which are invariant under the action of the unitary group. In Brackx et al. (2009) [8] a Clifford-Cauchy integral representation formula for h-monogenic functions has been established in the case of domains with smooth boundary, however the approach followed cannot be extended to the case where the boundary of the considered domain is fractal. At present, we investigate an alternative approach which will enable us to define in this case a Hermitian Cauchy integral over a fractal closed surface, leading to several types of integral representation formulae, including the Cauchy and Borel-Pompeiu representations. 相似文献
13.
We consider the Dirac particle that lives in the 1-dimensional configuration space consisting of two quantum wires and a junction between the two. We regard the spin of a Dirac particle as spintronic qubit. We give concrete formulae explicitly expressing the one-to-one correspondence between every self-adjoint extension of the minimal Dirac operator and its corresponding boundary condition of the wave functions of the Dirac particle. We then show that all the boundary conditions can be classified into just two types. The two types are characterized by whether the electron passes through the junction or not. We also show how the tunneling produces its own phase factor and what is the relation between the phase factor and the spintronic qubit in the tunneling boundary condition. 相似文献
14.
The paper deals with conformally invariant higher‐order operators acting on spinor‐valued functions, such that their symbols are given by powers of the Dirac operator. A general classification result proves that these are unique, up to a constant multiple. A general construction for such an invariant operators on manifolds with a given conformal spin structure was described in (Conformally Invariant Powers of the Ambient Dirac Operator. ArXiv math.DG/0112033, preprint), generalizing the case of powers of the Laplace operator from (J. London Math. Soc. 1992; 46 :557–565). Although there is no hope to obtain explicit formulae for higher powers of the Laplace or Dirac operator on a general manifold, it is possible to write down an explicit formula on Einstein manifolds in case of the Laplace operator (see Laplacian Operators and Curvature on Conformally Einstein Manifolds. ArXiv: math/0506037, 2006). Here we shall treat the spinor case on the sphere. We shall compute the explicit form of such operators on the sphere, and we shall show that they coincide with operators studied in (J. Four. Anal. Appl. 2002; 8 (6):535–563). The methods used are coming from representation theory combined with traditional Clifford analysis techniques. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
15.
We show that the non-embedded eigenvalues of the Dirac operator on the real line with complex mass and non-Hermitian potential V lie in the disjoint union of two disks, provided that the L 1-norm of V is bounded from above by the speed of light times the reduced Planck constant. The result is sharp; moreover, the analogous sharp result for the Schrödinger operator, originally proved by Abramov, Aslanyan and Davies, emerges in the nonrelativistic limit. For massless Dirac operators, the condition on V implies the absence of non-real eigenvalues. Our results are further generalized to potentials with slower decay at infinity. As an application, we determine bounds on resonances and embedded eigenvalues of Dirac operators with Hermitian dilation-analytic potentials. 相似文献
16.
Jean Dolbeault Maria J. Esteban Javier Duoandikoetxea Luis Vega 《Annales Scientifiques de l'école Normale Supérieure》2007,40(6):885-900
We prove some Hardy type inequalities related to the Dirac operator by elementary methods, for a large class of potentials, which even includes measure valued potentials. Optimality is achieved by the Coulomb potential. When potentials are smooth enough, our estimates provide some spectral information on the operator. 相似文献
17.
F. Brackx H. De Schepper M. E. Luna-Elizarrarás M. Shapiro 《Complex Analysis and Operator Theory》2012,6(2):325-339
Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis.
The theory is centred around the concept of monogenic functions, which constitute the kernel of a first order vector valued,
rotation invariant, differential operator ?{\underline{\partial}} called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has emerged as a new
branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on a subclass of monogenic functions,
i.e. the simultaneous null solutions, called Hermitean (or h−) monogenic functions, of two Hermitean Dirac operators ?z{\partial_{\underline{z}}} and ?zf{\partial_{\underline{z}^\dagger}} which are invariant under the action of the unitary group, and constitute a splitting of the original Euclidean Dirac operator.
In Euclidean Clifford analysis, the Clifford–Cauchy integral formula has proven to be a corner stone of the function theory,
as is the case for the traditional Cauchy formula for holomorphic functions in the complex plane. Also a Hermitean Clifford–Cauchy
integral formula has been established by means of a matrix approach. Naturally Cauchy integral formulae rely upon the existence
of fundamental solutions of the Dirac operators under consideration. The aim of this paper is twofold. We want to reveal the
underlying structure of these fundamental solutions and to show the particular results hidden behind a formula such as, e.g.
?E = d{\underline{\partial}E = \delta}. Moreover we will refine these relations by constructing fundamental solutions for the differential operators issuing from
the Euclidean and Hermitean Dirac operators by splitting the Clifford algebra product into its dot and wedge parts. 相似文献
18.
In this note p(D) = Dm+ b1Dm 1+···+ bmis a polynomial Dirac operator in R~n, where D =nj=1ej xjis a standard Dirac operator in Rn, bjare the complex constant coefficients. In this note we discuss all decompositions of p(D) according to its coefficients bj,and obtain the corresponding explicit Cauchy integral formulae of f which are the solution of p(D)f = 0. 相似文献
19.
We carry out the spectral analysis of singular matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the perturbations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Constant, periodic as well as diverging magnetic fields are covered, and Coulomb potentials up to the physical nuclear charge Z<137 are allowed. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods. 相似文献