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1.
《Stochastic Processes and their Applications》2020,130(10):6064-6093
It is shown in Li and Ying (2019) that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in the representation above. Finally applying previous results, we shall prove that every regular and local Dirichlet form has a special standard core generated by a continuous and strictly increasing function. 相似文献
2.
We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results. 相似文献
3.
《Mathematische Nachrichten》2017,290(17-18):2977-2991
Essential and continuous spectrum of symmetric difference equations have been investigated. It has been shown that the deficiency indices and the existence of these components of the spectrum are determined by the growth conditions of the coefficients. In particular, the deficiency indices are superimposition of those clusters determined by the coefficient growth. Finally, we have proved the neccessary and sufficient conditions for the existence of essential spectrum of selfadjoint subspace extensions using subspace theory and asymtotic summation. 相似文献
4.
B.Yousefi 《数学物理学报(B辑英文版)》2011,31(1):68-72
This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk. 相似文献
5.
Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of (I - PN)PM, 相似文献
6.
R. Srinivasan Puri Denise Morrey Andrew J. Bell John F. Durodola Evgenii B. Rudnyi Jan G Korvink 《Applied Mathematical Modelling》2009
A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS. 相似文献
7.
This paper mainly concerns a tuple of multiplication operators
defined on the weighted and unweighted multi-variable Bergman
spaces, their joint reducing subspaces and the von Neumann algebra
generated by the orthogonal projections onto these subspaces. It is
found that the weights play an important role in the structures of
lattices of joint reducing subspaces and of associated von Neumann
algebras. Also, a class of special weights is taken into account.
Under a mild condition it is proved that if those multiplication
operators are defined by the same symbols, then the corresponding
von Neumann algebras are $*$-isomorphic to the one defined on the
unweighted Bergman space. 相似文献
8.
Affine monotone and maximal monotone subspaces are characterized. 相似文献
9.
Albert Compta Josep Ferrer Marta Peña 《Mathematical Methods in the Applied Sciences》2011,34(3):309-314
Given ?? an (A,B)‐invariant subspace, we prove that the set of friend feedbacks is a linear variety, which can be considered as the direct sum of the feedbacks of the restriction to ?? and the co‐restriction to ??⊥. In particular, when the natural controllability hypothesis hold, both pole assignments are simultaneously possible by means of a convenient friend feedback. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
讨论了一维不可约强局部Dirichlet,型的正则子空间的Mosco收敛性.如果正则子空间的特征集是收敛的,那么相应的正则子空间在Mosco意义下也是收敛的.最后,用一些具体的例子说明了Mosco收敛不能保持Dirichlet型整体特性的稳定. 相似文献