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11.
B. Misra 《Journal of statistical physics》1987,48(5-6):1295-1320
It is widely recognized that for highly unstable dynamical systems there exists a fundamental limitation on predictability and determinism. An important class of such highly unstable systems is the class of K-flow, which is further characterized by the existence of time-asymmetric objects in the form of K-partition. Our recent approach to the problem of irreversibility has shown that when the implications of the limitation on determinism arising from strong form of instability and those of the existence of K-partition are consistently taken into account, one is naturally led from the physically unrealizable deterministic evolution of phase points to an entropy-increasing stochastic Markovian evolution. Furthermore, this transition is not the result of extraneously imposed coarse graining and/or approximation schemes, but can be brought about by an invertible transformation whose existence and construction are determined by the nature of the instability of the dynamical system itself. After a brief review of this theory which also contains some relatively new remarks, we prove that classical Klein-Gordon field (both massive and massless) possess the structure of K-flow. This seems to provide the first examples of relativistic systems that are K-flows. Some of the implications of this result are briefly discussed. From a mathematical point of view, this seems to be a first step toward an ergodic theory of partial differential equations. In the process, we also provide an independant group-theoretic proof of the existence of incoming and outgoing subspaces of the scattering theory of Lax and Phillips for the wave equation. 相似文献
12.
Ramiro Pino Olivier Bokanowski Eduardo V. Ludeña Roberto López Boada 《Theoretical chemistry accounts》2007,118(3):557-561
Bearing in mind the insight into the Hohenberg–Kohn theorem for Coulomb systems provided recently by Kryachko (Int J Quantum
Chem 103:818, 2005), we present a re-statement of this theorem through an elaboration on Lieb’s proof as well as an extension
of this theorem to finite subspaces.
Contribution to the Serafin Fraga Memorial Issue. 相似文献
13.
《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
14.
15.
A. K. Ramazanov 《Mathematical Notes》1999,66(5):613-627
Suppose thatD={z:|z|<1}, L
2
(D) is the space of functions square-integrable over area inD,A
k
(D) is the set of allk-analytic functions inD, (A
1
(D)=A(D) is the set of all analytic functions inD),A
k
L
2
(D)=L
2
(D)∩A
k
(D),A
1
L
2
(D)=AL
2
(D),
. It is proved that the subspacesA
k
L
2
0
(D),k=1, 2,..., are orthogonal to one another and the spaceA
m
L
2
(D) is the direct sum of such subspaces fork=1, 2,...,m. The kernel of the orthogonal projection operator from the spaceA
m
L
2
(D) onto its subspacesA
k
L
2
0
(D) is obtained. These results are applied to the study of the properties of polyrational functions of best approximation in
the metricL
2
(D).
Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 741–759, November, 1999. 相似文献
16.
The Wigner's Theorem states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex
Hilbert space which preserves orthogonality is induced by either a unitary or an anti-unitary operator. There exist many Wigner-type
theorems, in particular in indefinite metric spaces, von Neumanns algebras and Banach spaces and we try to find a common origin
of all these results by using properties of the lattice subspaces of certain topological vector spaces. We prove a Wigner-type
theorem for a pair of dual spaces which allows us to obtain, as particular cases, the usual Wigner's Theorem and some of its
generalizations.
PACS: 02.40.Dr, 03.65.Fd,03.65.Ta
AMS Subject Classification (1991): 06C15, 46A20, 81P10. 相似文献
17.
In a Hilbert space, there exists a natural correspondence between continuous projections and particular pairs of closed subspaces.
In this paper, we generalize this situation and associate to a symmetric lattice L a subset P(L) of L× L, called its projection poset. If L is the lattice of closed subspaces of a topological vector space then elements of P(L) correspond to continuous projections and we prove that automorphisms of P(L) are determined by automorphisms of the lattice L when this lattice satisfies some basic properties of lattices of closed subspaces.
Primary: 06C15, Secondary: 03G12 81P10. 相似文献
18.
Michael Lauzon 《Journal of Functional Analysis》2004,212(2):500-512
In this paper we find a necessary and sufficient condition for two closed subspaces, and , of a Hilbert space to have a common complement, i.e. a subspace having trivial intersection with and and such that .Unlike the finite-dimensional case the condition is significantly more subtle than simple equalities of dimensions and codimensions, and non-trivial examples of subspaces without a common complement are possible. 相似文献
19.
In this paper the author writes a simple characterization for the best copositive approximation in c; the space of convergent sequences, by elements of finite dimensional Chebyshev subspaces, and shows that it is unique. 相似文献
20.
We show the existence of a rank function on finitely generated modules over group algebras , where is an arbitrary field and is a finitely generated amenable group. This extends a result of W. Lück (1998).