共查询到20条相似文献,搜索用时 296 毫秒
1.
We consider infinite products in K-homology. We study these products in relation with operators on filtered Hilbert spaces, and infinite iterations of universal constructions on C*-algebras. In particular, infinite tensor power of extensions of pseudodifferential operators on R are considered. We extend anti-Wick pseudodifferential operators to infinite tensor products of spaces of the type L
2(R), and compare our infinite tensor power construction with an extension of pseudodifferential operators on R
. We show that the K-theory connecting maps coincide. We propose a natural definition of ellipticity for anti-Wick operators on R, compute the corresponding index, and draw some consequences concerning these operators. 相似文献
2.
J. Barral M. -O. Coppens B. B. Mandelbrot 《Journal de Mathématiques Pures et Appliquées》2003,82(12):1555-1589
A nonnegative 1-periodic multifractal measure on
is obtained as infinite random product of harmonics of a 1-periodic function W(t). Such infinite products are statistically self-affine and generalize certain Riesz products with random phases. They are martingale structures, therefore converge. The criterion on W for nondegeneracy is provided. It differs completely from those for other known random measures constructed as martingale limits of multiplicative processes. In particular, it is very sensitive to small changes in W(t). When these infinite products are interpreted in the framework of thermodynamic formalism for random transformations, logW is a potential function when W>0. For regular enough potentials, in case of degeneracy, the natural normalization makes the sequence of measures converge. Moreover, this normalization is neutral for nondegenerate martingales. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points. 相似文献
3.
Let H be a complex Hilbert space with dimH ≥3, Bs(H) the (real) Jordan algebra of all self-adjoint operators on H. Every surjective map Ф : Bs(H)→13s(H) preserving numerical radius of operator products (respectively, Jordan triple products) is characterized. A characterization of surjective maps on Bs (H) preserving a cross operator norm of operator products (resp. Jordan triple products of operators) is also given. 相似文献
4.
We study conditions on an infinite dimensional separable Banach space X implying that X is the only non-trivial invariant subspace of X** under the action of the algebra
of biconjugates of bounded operators on
. Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of c
0, and show in particular that any space which does not contain ℓ1 and has property (u) of Pelczynski is simple. 相似文献
5.
We investigate the notion of complexity for finitely presented groups and the related notion of complexity for three‐dimensional manifolds. We give two‐sided estimates on the complexity of all the Milnor groups (the finite groups with free action on S3), as well as for all finite Abelian groups. The ideas developed in the process also allow to construct two‐sided bounds for the values of the so‐called T ‐invariant (introduced by Delzant) for the above groups, and to estimate from below the value of T ‐invariant for an arbitrary finitely presented group. Using the results of this paper and of previous ones, we then describe an infinite collection of Seifert threemanifolds for which we can asymptotically determine the complexity in an exact fashion up to linear functions. We also provide similar estimates for the complexity of several infinite families of Milnor groups. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
Egon Scheffold 《Acta Mathematica Hungarica》2005,108(1-2):13-23
Summary Certain bounded linear operators from Hilbert spaces H into function spaces C(X) are approximated by operators of finite rank with the aid of orthogonal projections. As examples for such operators we present special integral operators and linear partial differential operators. As application we consider a collocation method. 相似文献
7.
Gunnar Carlsson 《K-Theory》1995,9(4):305-322
Although theK-theory functor on the category of symmetric monoidal categories preserves finite products for essentially trivial reasons, this is not so in the case of infinite products. In this paper, we show that in factK-theory does preserve infinite products, but for non-trivial reasons.Supported in part by NSF DMS 9209714. 相似文献
8.
Stanislav Shkarin 《Journal of Mathematical Analysis and Applications》2010,367(2):713-856
We give a short proof of existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Fréchet space. Similar argument provides disjoint dual hypercyclic tuples of operators of any length on any infinite dimensional Banach space with separable dual. 相似文献
9.
Existence of solutions of infinite systems of differential equations of general order with boundary conditions in the spaces c0 and ℓ1 via the measure of noncompactness 下载免费PDF全文
《Mathematical Methods in the Applied Sciences》2018,41(10):3558-3569
The aim of this paper is to obtain existence results for an infinite system of differential equations of order n with boundary conditions in the Banach spaces c0 and ℓ1 with the help of a technique associated with measures of noncompactness. We also provide some illustrative examples in support of our existence theorems. 相似文献
10.
Peggy Tang Strait 《Journal of multivariate analysis》1974,4(4):494-496
It is shown that if X1, X2, …, Xn are symmetric random variables and max(X1, …, Xn)+ = max(0, X1, …, Xn), then E[max(X1,…,Xn)+]=[max(X1,X1,+X2,+X1,+X3,…X1,+Xn)+], and in the case of independent identically distributed symmetric random variables, E[max(X1, X2)+] = E[(X1)+] + (1/2)E[(X1 + X2)+], so that for independent standard normal random variables, E[max(X1, X2)+] = (1/√2π)[1 + (1/√2)]. 相似文献
11.
Kluppelberg[1], Asmussen 等[2] 研究了增量有有限负均值的随机游动上确界的密度的渐近性. 该文则在 Denisov 等[3], 程东亚和王岳宝[4]的基础上, 进一步研究了增量均值为负无穷的随机游动上确界的密度的渐近性. 最后, 为了说明常见重尾分布大多满足上述结果的条件, 该文给出了一些分布族的性质. 相似文献
12.
Jens Marklof Yves Tourigny Lech Wolowski 《Transactions of the American Mathematical Society》2008,360(7):3391-3427
We construct explicit invariant measures for a family of infinite products of random, independent, identically-distributed elements of SL. The matrices in the product are such that one entry is gamma-distributed along a ray in the complex plane. When the ray is the positive real axis, the products are those associated with a continued fraction studied by Letac & Seshadri [Z. Wahr. Verw. Geb. 62 (1983) 485-489], who showed that the distribution of the continued fraction is a generalised inverse Gaussian. We extend this result by finding the distribution for an arbitrary ray in the complex right-half plane, and thus compute the corresponding Lyapunov exponent explicitly. When the ray lies on the imaginary axis, the matrices in the infinite product coincide with the transfer matrices associated with a one-dimensional discrete Schrödinger operator with a random, gamma-distributed potential. Hence, the explicit knowledge of the Lyapunov exponent may be used to estimate the (exponential) rate of localisation of the eigenstates.
13.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2001,47(2):205-210
We show that the axiom of choice AC is equivalent to the Vector Space Kinna‐Wagner Principle, i.e., the assertion: “For every family 𝒱= {Vi : i ∈ k} of non trivial vector spaces there is a family ℱ = {Fi : i ∈ k} such that for each i ∈ k, Fi is a non empty independent subset of Vi”. We also show that the statement “every vector space over ℚ has a basis” implies that every infinite well ordered set of pairs has an infinite subset with a choice set, a fact which is known not to be a consequence of the axiom of multiple choice MC. 相似文献
14.
Let G be a group with a set of operators such that Z(G) is -admissible. Central -automorphisms occur in the Krull-Remak-Schmidt Theorem. We discuss the existence of a central -endomorphism of G that is not an automorphism.2000 Mathematics Subject Classification: 20E36 相似文献
15.
We study a semigroup of linear operators on a Banach space X which satisfies the condition codim X
0<, where
We show that X
0 is closed and establish some properties of the asymptotic behavior of the subspaces complementing X
0 to X. 相似文献
16.
E. G. Zelenyuk 《Mathematical Notes》2000,67(5):599-602
It is proved that any infinite Abelian group with finitely many elements of order two can be partitioned into two subsets
that are dense in any nondiscrete group topology, and hence contain no cosets of infinite subgroups.
Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 706–711, May, 2000. 相似文献
17.
If G is a group and if the upper hypercenter, Z, of G is such that G∕Z is finite then a recent theorem shows that G contains a finite normal subgroup L such that G∕L is hypercentral. The purpose of the current paper is to obtain a version of this result for subgroups G of GL(F,A), when A is an infinite dimensionalF-vector space. 相似文献
18.
A real square matrix A is called a P-matrix if all its principal minors are positive. Such a matrix can be characterized by the sign non-reversal property. Taking a cue from this, the notion of a P-operator is extended to infinite dimensional spaces as the first objective. Relationships between invertibility of some subsets of intervals of operators and certain P-operators are then established. These generalize the corresponding results in the matrix case. The inheritance of the property of a P-operator by the Schur complement and the principal pivot transform is also proved. If A is an invertible M-matrix, then there is a positive vector whose image under A is also positive. As the second goal, this and another result on intervals of M-matrices are generalized to operators over Banach spaces. Towards the third objective, the concept of a Q-operator is proposed, generalizing the well known Q-matrix property. An important result, which establishes connections between Q-operators and invertible M-operators, is proved for Hilbert space operators. 相似文献
19.
Hiroshi Isozaki 《偏微分方程通讯》2013,38(7):625-655
By using a time slicing procedure, we represent the solution operator of a second-order parabolic pseudodifferential equation on ? n as an infinite product of zero-order pseudodifferential operators. A similar representation formula is proven for parabolic differential equations on a compact Riemannian manifold. Each operator in the multi-product is given by a simple explicit Ansatz. The proof is based on an effective use of the Weyl calculus and the Fefferman-Phong inequality. 相似文献
20.
Suppose that X1, X2,…, Xn are independently distributed according to certain distributions. Does the distribution of the maximum of {X1, X2,…, Xn} uniquely determine their distributions? In the univariate case, a general theorem covering the case of Cauchy random variables is given here. Also given is an affirmative answer to the above question for general bivariate normal random variables with non-zero correlations. Bivariate normal random variables with nonnegative correlations were considered earlier in this context by T. W. Anderson and S. G. Ghurye. 相似文献