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131.
Jipu Ma 《中国科学A辑(英文版)》1997,40(12):1233-1238
A generalized dimension is further developed. Here subtraction and addition of two generalized dimensions are defined, so
that the operations: ∞ ± n = ∞, ∞ + ∞ = ∞, which used to play an inflexible role, are refined and moreover, ∞ - ∞, which used
to be meaningless, is done in sense. Then generalized index for semi-Fred-holm operators is developed to wholeB(H), i.e. all of bounded linear operators in Hilbert spaceH. Theorem 2.2 is proved with an example, which is in contradiction to a known proposition for semi-Fredholm operators in form,
practically a refined result of the known proposition. Then, it is proved thatB(H) is the union of countably many disjoint arewise connected sets over all the generalized dimensions ofB(H).
Project supported by the National Natural Science Foundation of China 相似文献
132.
In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu. 相似文献
133.
In this paper,applying the concept of generalized KKM map,we study problems ofvariational inequalities.We weaken convexity(concavity)conditions for a functional of two variables■(x,y)in the general variational inequalities.Last,we show a proof of non-topological degree meth-od of acute angle principle about monotone operator as an application of these results. 相似文献
134.
Steven J. Sepanski 《Journal of Theoretical Probability》1997,10(4):1053-1063
For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator. 相似文献
135.
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
136.
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
137.
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
138.
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
139.
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
140.
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