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131.
Operator Matrix Forms of Positive Operators 总被引:2,自引:0,他引:2
If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2)of operators on Hibert spaces is given,we proved that the operator ~↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R(A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet. 相似文献
132.
Shih-Sen ChangB. S. LeeYu-Qing Chen 《Applied Mathematics Letters》1995,8(6):29-34
The purpose of this paper is to study the existence problem of solutions and perturbation problem for some kind of variational inequalities with monotone operators in nonreflexive Banach spaces, and to obtain some results. 相似文献
133.
A classical Fermi accelerator model (FAM) is known to show chaotic behavior. The FAM is defined by a free particle bouncing elastically from two rigid walls, one fixed and the other oscillating periodically in time. The central aim of this paper is to connect the quantum and the classical solutions to the FAM in the semiclassical limit. This goal is accomplished using a finite inverted parametric oscillator (FIPO), confined to a box withfixed walls, as an alternative representation of the FAM. In the FIPO representation, an explicit correspondence between classical and quantum limits is accomplished using a Husimi representation of the quasienergy eigenfunctions. 相似文献
134.
Alfred Wünsche 《Annalen der Physik》1992,504(3):181-197
The eigenvalue problem for arbitrary linear combinations kα + μα? of a boson annihilation operator α and a boson creation operator α? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter. 相似文献
135.
在本文中,我们讨论了带作用群的群系的临界结构,给出了处理允许某些作用群的群的问题的一般方法,作为应用,我们特别给出了关于幂零群及p-幂零群的一些结果。 相似文献
136.
刘永民 《数学物理学报(A辑)》2004,24(3):375-380
讨论了 C\+n 中有界对称域的加权Bergman空间上符号属于 L\+2\-a(Ω, dV\-λ) 的小Hankel算子, 利用符号 Φ 的某种积分变换,给出了小Hankel算子 h\-Φ 属于Schatten理想 S\-p 的特征. 相似文献
137.
该文通过一种基本的分析方法,得到了一类退化型Schrodinger方程解的连续性结果,方程的类型为:Lu+vu=(f_i)_{x_i},其中L为一退化椭圆算子,v属于某一Kato类的类比,而f_i 属于某一加权L^p空间. 相似文献
138.
Let (0 < α < n) be the generalized commutator generated by fractional integral with rough kernel and the m–th order remainder of the Taylor formula of a function A. In this paper, the (Lp, Lr) (r > 1) boundedness, the weak (L1, Ln/(n–α–β)) boundedness and the (Lp, ?β, ∞p) boundedness of are discussed, when DγA belongs to the Lipschitz function spaces. 相似文献
139.
Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K
A
of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K
A
and SA is deduced. Furthermore, the rigidity of the functor K
A
is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed. 相似文献
140.
Hubert Kalf 《Journal of Differential Equations》2004,205(2):408-423
We show that the point spectrum of the standard Coulomb-Dirac operator H0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment Ha as the anomaly parameter tends to 0. For negative angular momentum quantum number κ, this holds for all Coulomb coupling constants c for which H0 has a distinguished self-adjoint realisation. For positive κ, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H0 and the limits of eigenvalues of Ha appears, accompanied with additional oscillations of the eigenfunctions of Ha very close to the origin. 相似文献