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1.
Let B be a Brownian motion, and let be the space of all continuous periodic functions f with period 1. It is shown that the set of all f such that the stochastic convolution does not have a modification with bounded trajectories, and consequently does not have a continuous modification, is of the second Baire category.  相似文献   

2.
Let μ n be a sequence of random finite signed measures on the locally compact group G equal to either or ℝ d . We give weak conditions on the sequence μ n and on functions K such that the convolution product μ n *K, and its derivatives, converge in law, in probability, or almost surely in the Banach spaces or L p (G). Examples for sequences μ n covered are the empirical process (possibly arising from dependent data) and also random signed measures where is some (nonparametric) estimator for the measure ℙ, including the usual kernel and wavelet based density estimators with MISE-optimal bandwidths. As a statistical application, we apply the results to study convolutions of density estimators.   相似文献   

3.
The Rankin-Selberg convolution is usually normalized by the multiplication of a zeta factor. One naturally expects that the non-normalized convolution will have poles where the zeta factor has zeros, and that these poles will have the same order as the zeros of the zeta factor. However, this will only happen if the normalized convolution does not vanish at the zeros of the zeta factor. In this paper, we prove that given any point inside the critical strip, which is not equal to and is not a zero of the Riemann zeta function, there exist infinitely many cusp forms whose normalized convolutions do not vanish at that point.

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4.
We investigate the asymptotic behavior of a sequence of convolutionsv (n 1() ** n (), where { n } n=1 is some random process taking values in a semigroupM 1(S) of probability Borel measures on a compact topological semigroupS.  相似文献   

5.
LetE denote a real separable Banach space and letZ=(Z(t, f) be a family of centered, homogeneous, Gaussian independent increment processes with values inE, indexed by timet0 and the continuous functionsf:[0,t] E. If the dependence ont andf fulfills some additional properties,Z is called a gaussian random field. For continuous, adaptedE-valued processesX a stochastic integral processY = 0 . Z(t, X)(dt) is defined, which is a continuous local martingale with tensor quadratic variation[Y] = 0 . Q(t, X)dt, whereQ(t, f) denotes the covariance operator ofZ(t, f).Y is called a solution of the homogeneous Gaussian martingale problem, ifY = 0 . Z(t, Y)(dt). Such solutions occur naturally in connection with stochastic differential equations of the type (D):dX(t)=G(t, X) dt+Z(t, X)(dt), whereG is anE-valued vector field. It is shown that a solution of (D) can be obtained by a kind of variation of parameter method, first solving a deterministic integral equation only involvingG and then solving an associated homogeneous martingale problem.  相似文献   

6.
7.
Guédon  Olivier 《Positivity》1997,1(1):1-5
Using Gordon's inequalities, we give a short proof of the existence of an embedding T:l2k to ln such that ||T||||T-1|| c k/ln(1+n/k). In the same way, we give a new proof of a theorem of Milman and Schechtman (1995).  相似文献   

8.
Tyurin  V. M. 《Mathematical Notes》2002,72(5-6):833-840
For linear differential operators with coefficients of class C on n, we prove theorems on the simultaneous invertibility and equivalence of spectra in the Lebesgue space L p, Stepanov space M p, and in a particular Banach space V p L p, p 1  相似文献   

9.
In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.  相似文献   

10.
Let u(x) xR q be a symmetric nonnegative definite function which is bounded outside of all neighborhoods of zero but which may have u(0)=. Let p x, (·) be the density of an R q valued canonical normal random variable with mean x and variance and let {G x, ; (x, )R q ×[0,1 ]} be the mean zero Gaussian process with covariance
A finite positive measure on R q is said to be in with respect to u, if
When , a multiple Wick product chaos is defined to be the limit in L 2, as 0, of
where
,
denotes the Wick product of the m j normal random variables .Consider also the associated decoupled chaos processes , defined as the limit in L 2, as 0, of
where are independent copies of G x,.Define
Note that a neighborhood of the diagonals of in is excluded, except those points on the diagonal which originate in the same Wick product in (i). Set
One of the main results of this paper is: Theorem A. If is continuous on (R q ) r for all then is continuous on .When u satisfies some regularity conditions simple sufficient conditions are obtained for the continuity of on (R q ) r . Also several variants of (i) are considered and related to different types of decoupled processes. These results have applications in the study of intersections of Lévy process and continuous additive functionals of several Lévy processes.  相似文献   

11.
关于幂等阵的相似与线性组合   总被引:3,自引:0,他引:3  
宁群 《大学数学》2004,20(3):84-86
证明了数域上两个同阶幂等阵相似的充要条件是它们有相同的秩;给出了幂等阵的相似标准型;讨论了两个幂等阵的线性组合仍是幂等阵的充要条件.  相似文献   

12.
Abstract

In this work, we shall investigate solution (strong, weak and mild) processes and relevant properties of stochastic convolutions for a class of stochastic retarded differential equations in Hilbert spaces. We introduce a strongly continuous one-parameter family of bounded linear operators which will completely describe the corresponding deterministic systematical dynamics with time delays. This family, which constitutes the fundamental solutions (Green's operators) of our stochastic retarded systems, is applied subsequently to define mild solutions of the stochastic retarded differential equations considered. The relations among strong, weak and mild solutions are explored. By virtue of a strong solution approximation method, Burkholder–Davis–Gundy's type of inequalities for stochastic convolutions are established.  相似文献   

13.
苏维钢 《东北数学》2006,22(2):233-240
This paper discusses the special properties of the spectrum of linear operators (in particular, bounded linear operators) on quotient indecomposable Banach spaces; shows that in such spaces generators of Co-groups are always bounded linear operators, and that generators of Co-semigroups satisfy the spectral mapping theorem; and gives an example to show that the generators of Co-semigroups in quotient indecomposable spaces are not necessarily bounded.  相似文献   

14.
On K_0-groups of operator algebras on Banach spaces   总被引:1,自引:0,他引:1  
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.  相似文献   

15.
A concept of a fundamental solution is introduced for linear operator equations given in some functional spaces. In the case where this fundamental solution does not exist, the representation of the solution is found by the concept of a generalized fundamental solution, which is introduced for operators with nontrivial and generally infinite-dimensional kernels. The fundamental and generalized fundamental solutions are also investigated for a class of Fredholm-type operator equations. Some applications are given for one-dimensional generally nonlocal hyperbolic problems with trivial, finite- and infinite-dimensional kernels. The fundamental and generalized fundamental solutions of such problems are constructed as particular solutions of a system of integral equations or an integral equation. These fundamental solutions become meaningful in a general case when the coefficients are generally nonsmooth functions satisfying only some conditions such as p-integrablity and boundedness.  相似文献   

16.
张利  楚秀娇 《数学学报》2021,64(1):139-144
设λi(i= 1,..,N)是一列非0的数,D是一维复平面C的开单位圆盘,φi (i = 1,...,N)是D的解析自映射,本文研究了定义在加权Bloch空间上复合算子线性组合∑Ni=1λiCψi的紧致性.  相似文献   

17.
This paper gives some relations and properties of several kinds of generalized convexity in Banach spaces. As a result, it proves that every kind of uniform convexity implies the Banach-Sakes property, and several notions of uniform convexity in literature are actually equivalent.  相似文献   

18.
In this paper suitable linear combinations for a multivariate extension of the generalized sampling series are considered, also in the Kantorovich version. These combinations provide a better order of approximation. Finally the particular example of the Bochner-Riesz kernel is discussed.  相似文献   

19.
研究了Banach空间中广义逆的扰动问题.给出了广义逆稳定的一些新特征,进而证明了这些稳定性特征与广义逆的选取无关,并由此得到了广义逆作为集值映射是下半连续的充要条件.  相似文献   

20.
严锴  苏维钢 《应用数学》2012,25(3):655-660
定义了四种新的谱性质:性质(y),性质(gy),性质(by),性质(gby),从而再次推广了Weyl型定理,并探讨了这四种新性质同Weyl型定理及其推广性质之间的关系.  相似文献   

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