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91.
We give a geometric proof of the following well-established theorem for o-minimal expansions of the real field: the Hausdorff limits of a compact, definable family of sets are definable. While previous proofs of this fact relied on the model-theoretic compactness theorem, our proof explicitly describes the family of all Hausdorff limits in terms of the original family. 相似文献
92.
Horst Osswald 《Advances in Mathematics》2003,176(1):1-37
Using infinitesimals, we develop Malliavin calculus on spaces which result from the classical Wiener space by replacing with any abstract Wiener space .We start from a Brownian motion b on a Loeb probability space Ω with values in the Banach space is the standard part of a ∗finite-dimensional Brownian motion B. Then we define iterated Itô integrals as standard parts of internal iterated Itô integrals. The integrator of the internal integrals is B and the values of the integrands are multilinear forms on , where is a ∗finite-dimensional linear space over between the Hilbert space and its ∗-extension .In the first part we prove a chaos decomposition theorem for L2-functionals on Ω that are measurable with respect to the σ-algebra generated by b. This result yields a chaos decomposition of L2-functionals with respect to the Wiener measure on the standard space of -valued continuous functions on [0,1]. In the second part we define the Malliavin derivative and the Skorohod integral as standard parts of internal operators defined on ∗finite-dimensional spaces. In an application we use the transformation rule for finite-dimensional Euclidean spaces to study time anticipating and non-anticipating shifts of Brownian motion by Bochner integrals (Girsanov transformations). 相似文献
93.
94.
It is shown that all Banach space operators which have Fourier
type p(1 < p 2) with respect to a second countable
locally compact abelian group G also have
Fourier type p with
respect to every closed discrete subgroup H
of G. The same
statement holds for any closed subgroup H
of G when p = 2.
Also shown as a corollary is that Fourier type 2 operators have
Walsh type 2.
Received: 10 June 2002 相似文献
95.
Daniel Markiewicz 《Journal of Functional Analysis》2003,200(1):237-280
Given a W∗-continuous semigroup φ of unital, normal, completely positive maps of B(H), we introduce its continuous tensor product system . If α is a minimal dilation E0-semigroup of φ with Arveson product system F, then is canonically isomorphic to F. We apply this construction to a class of semigroups of arising from a modified Weyl-Moyal quantization of convolution semigroups of Borel probability measures on . This class includes the heat flow on the CCR algebra studied recently by Arveson. We prove that the minimal dilations of all such semigroups are completely spatial, and additionally, we prove that the minimal dilation of the heat flow is cocyle conjugate to the CAR/CCR flow of index two. 相似文献
96.
A new construction of combings is used to distinguish
between several previously indistinguishable
classes of groups associated to the theory of automatic groups
and non-positive curvature in group theory.
We construct synchronously bounded combings for a class
of groups that are neither bicombable nor automatic.
The linguistic complexity of these combings is
analysed: in many cases the language of words
in the combing is an indexed language. 相似文献
97.
Ralf Schindler 《Monatshefte für Mathematik》2003,139(4):335-340
We state different versions of the P=?NP problem for infinite time Turing machines. It is observed that PNP collapses to the fact that there are analytic sets which are not Borel.The author thanks J. D. Hamkins, R. Schipperus, and P. Welch for comments on earlier versions of this paper. He thanks Sanders Seliverstov for pointing out an inaccuracy in the first version of the proof of Theorem 2.10.Received April 19, 2002; in revised form June 10, 2002
Published online May 16, 2003 相似文献
98.
Norbert Sauer 《Combinatorica》2001,21(2):293-308
Dedicated to the memory of Paul Erdős
Erdős, Hajnal and Pósa exhibited in [1] a partition (U,D) of the edges of the Rado graph which is a counterexample to . They also obtained that if every vertex of a graph has either in or in the complement of finite degree then .
We will characterize all graphs so that .
Received October 29, 1999
RID="†"
ID="†" Supported by NSERC of Canada Grant #691325. 相似文献
99.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
100.
对移动终端中使用的信道译码技术进行了介绍,指出未来的移动终端需要支持多种通信标准。设计了一种用于移动终端的联合信道译码器,可支持多种通信标准,达到最大限度利用共享资源,从而节省总体成本。 相似文献