The Skorohod integral and the derivative operator of functional of a cylindrical Brownian motion

The paper presents a definition of the Skorohod integral of operator-valued processes and the derivative operator for functional of a cylindrical Brownian motionW on a Hilbert space. The method is based on the chaos expansions in terms of multiple Wiener integrals ofW.This research was partially supported by the U.S. Air Force Office of Scientific Research Contract No. F49620 85C 0144. The research of V. Pérez-Abreu was also supported by CONACYT Grant D111-904237.     

A localization argument for characters of reductive Lie groups

This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by Schmid (in: Deformation Theory and Symplectic Geometry, Mathematical Physics Studies, Vol. 20, Kluwer Academic Publishers, Dordrecht, 1997, pp. 259-270).A corresponding problem in the compact group setting was solved by Berline et al. (Heat Kernels and Dirac Operators, Springer, Berlin, 1992) by an application of the theory of equivariant forms and particularly the fixed point integral localization formula. This article (besides its representation-theoretical significance) provides a whole family of examples where it is possible to localize integrals to fixed points with respect to an action of a noncompact group. Moreover, a localization argument given here is not specific to the particular setting considered in this article and can be extended to a more general situation.There is a broadly accessible article (Libine, A Localization Argument for Characters of Reductive Lie Groups: An Introduction and Examples, 2002, math.RT/0208024) which explains how the argument works in the case, where the key ideas are not obstructed by technical details and where it becomes clear how it extends to the general case.     

On the commutator of the Marcinkiewicz integral

boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the and the boundedness for the commutator of the Marcinkiewicz integral are obtained.     

Weighted integral inequalities for conjugate A-harmonic tensors

We first prove a local weighted integral inequality for conjugate A-harmonic tensors. Then, as an application of our local result, we prove a global weighted integral inequality for conjugate A-harmonic tensors in L^s(μ)-averaging domains, which can be considered as a generalization of the classical result. Finally, we give applications of the above results to quasiregular mappings.     

Conditions for Choquet integral representation of the comonotonically additive and monotone functional

If the universal set X is not compact but locally compact, a comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is not represented by one Choquet integral, but represented by the difference of two Choquet integrals. The conditions for which a c.m. functional can be represented by one Choquet integral are discussed.     

齐型空间上交换子的紧性

设(x，d，μ)是齐型空间．本文证明了分数次积分算子Iα与VMO函数构成的交换子I^ba是L^p(X)到L^q(X)的紧算子，其中α∈(0，1)，1＜p＜q＜∞且1/q＝1/p—α。     

What is the Rees algebra of a module?

In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module may be computed in terms of a ``maximal' map from to a free module as the image of the map induced by on symmetric algebras. We show that the analytic spread and reductions of can be determined from any embedding of into a free module, and in characteristic 0--but not in positive characteristic!--the Rees algebra itself can be computed from any such embedding.

     

Inner bounds for the spectrum of quasinormal operators

A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.

     

On the inversion of the convolution and Laplace transform

We present a new inversion formula for the classical, finite, and asymptotic Laplace transform of continuous or generalized functions . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sense. The limit is uniform if is continuous, it is in if , and converges in an appropriate norm or Fréchet topology for generalized functions . As a corollary we obtain a new constructive inversion procedure for the convolution transform ; i.e., for given and we construct a sequence of continuous functions such that .

     

正交变换在重积分中某些应用

正交变换是代数学的基本内容 ,其用途十分广泛 .重积分的计算往往存在技术性的困难 ,若利用“正交变换”的有关理论去解决某些重积分的计算问题是颇有功效的 .本文将以“正交变换”为工具 ,简洁的处理重积分的某些问题