局部域上的仿交换算子与Schatten类性质

设Tb^s是局部域K上带符号b的仿交换算子，本文证明了当Tb^st定义式中函数A（ξ，η）满足一定的条件时，Tb^st∈Sp的充要条件是b∈Bp^s t 1/p。     

局部紧Vilenkin群上的仿积算子与仿线性化

建立了局部紧Vilenkin群上仿积算子的概念及其应用于非线性问题中的仿线性化方法.这类算子在处理不具有经典意义下导数的函数时将起重要作用.     

Heisenberg型群上的仿积算子

首先给出了Heisenberg型群上一类仿积算子的定义,研究了该算子的L~2→L~2有界性.其次探讨了Heisenberg型群上的Calderon-Zygmund算子,包括该算子的L~p→L~p有界性,L~1→L~(1,∞)有界性以及H~1→L~1有界性.最后证明了仿积算子也是Calderon-Zygmund算子,同时还证明了仿积算子的一些其它重要性质.     

仿微分算子的Εгоров定理

本文在文献[1]的基础上给出了仿微分算子的定理。这个定理对研究仿微分算子的许多性质是很重要的。为得到此定理,本文又引入了共轭仿Fourier积分算子概念,并讨论了有关性质。     

次线性奇异积分算子在局部域的Herz空间上的有界性

令 1 p ∞ ,0 0 ,K为局部域 .本文将着重讨论一类线性分数次积分算子在 Herz空间K (α,p,l;K )上的有界性     

以仿正规算子为参数的初等算子的性质

若对x∈H,‖Tx‖~2≤‖T~2x‖‖x‖,则称T是仿正规算子.d_(AB)表示δ_(AB)或△_(AB),其中δ_(AB)和△_(AB)分别表示Banach空间B(H)上的广义导算子和初等算子,其定义为δ_(AB)X=AX-XB,△_(AB)X=AXB-X,X∈B(H).若A和B~*是仿正规算子,则可证d_(AB)是polaroid算子,f∈H(σ(d_(AB))),f(d_(AB))满足广义Weyl定理,f(d_(AB)~*)满足广义a-Weyl定理,其中H(σ(d_(AB)))表示在σ(d_(AB))的某邻域上解析的函数全体.     

局部域上的局部Hardy空间

文献［１］，［２］，［３］中讨论了Ｒ^ｎ上的局部Ｈａｒｄｙ空间，并利用乘子定理证明了ｈ_ｐ（Ｒ^ｎ）＝Ｆ_p.2⁰（Ｒ^ｎ）．本文利用Ｃｈｅｂｙｓｈｅｖ等式及正则函数的性质证明了在局部域上有类似的结果ｈ_ｐ（Ｒ^ｎ）＝Ｆ_p.2⁰（Ｒ^ｎ），从而建立起函数空间之间的关系，并由此给出一个乘子定理．     

BMO鞅空间上极大算子与均方算子的有界性

本文证明了,q 均方算子在 X 值 BMO 鞅空间上是有界的当且仅当 X 同构于 q凸 Banach 空间。此外给出了极大算子与 q 均方算子的 BMO 范数,讨论了鞅空间(?)_q 与BMO_q 的相互包含关系并以此刻划了 Banach 空间的几何性质。     

Bergman空间上可交换的Hankel算子和Toeplitz算子

证明了Bergman空间上的两个小Hankel算子如果是可交换的且其中一个是拟齐次的小Hankel算子,则另一个也是拟齐次的.还研究了Toeplitz算子和小Hankel算子的交换性.     

局部域上的Herz型Besov空间

令K为局部域,Kn为K上n维向量空间.本文讨论Herz型Besov空间Kaq,pBsβ(Kn)的某些性质.     

Basic Results of Gabor Frame on Local Fields

Basic facts for Gabor frame {Eu(m)bTu(n)ag}m,n∈p on local field are investigated. Accurately, that the canonical dual of frame {Eu(m)bTu(n)ag}m,n∈p also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu(m)bTu(n)ag}m,n∈p to be a frame for L2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L2(K) are established. An example is finally given.     

局部域上Gabor紧框架的特征

主要讨论局部域上的Gabor紧框架.首先,建立局部域上Gabor系{xm(bx)g(x-u(n)a)}m.n∈p构成L~2(K)上紧框架的特征.其次,给出Gabor系{X_m(bx)g(x-u(n)a)}_(m,n∈p)成为L~2(K)上标准正交基的充要条件.     

Fourier Transform Over Local Fields

The Fourier transform in the space of distributions on finite-dimensional vector spaces over local fields is defined, and a strong similarity between the case of archimedian and non-archimedian fields is discussed. Furthermore, the definition of the Fourier transform for the case of “functions” on finite-dimensional vector spaces over 2-dimensional local fields is introduced. Leonardo da Vinci lecture held on June 29, 2005 Received: October 2005     

Construction Theory of Function on Local Fields

We establish the construction theory of function based upon a local field K p as underlying space. By virture of the concept of pseudo-differential operator, we introduce fractal calculus(or, p-type calculus, or, Gibbs-Butzer calculus). Then, show the Jackson direct approximation theorems, Bermstein inverse approximation theorems and the equivalent approximation theorems for compact group D( Kp) and locally compact group K+p(= Kp), so that the foundation of construction theory of function on local fields is established. Moreover, the Jackson type, Bernstein type,and equivalent approximation theorems on the H ?lder-type space Cσ(Kp), σ 0, are proved; then the equivalent approximation theorem on Sobolev-type space Wrσ(Kp),σ≥ 0, 1 ≤ r +∞, is shown.     

Some New Inequalities for Wavelet Frames on Local Fields

Wavelet frames have gained considerable popularity during the past decade,primarily due to their substantiated applications in diverse and widespread fields of science and engineering.Finding general and verifiable conditions which imply that the wavelet systems are wavelet frames is among the core problems in time-frequency analysis.In this article,we establish some new inequalities for wavelet frames on local fields of positive characteristic by means of the Fourier transform.As an application,an improved version of the Li-Jiang inequality for wavelet frames on local fields is obtained.     

Periodic Wavelet Frames on Local Fields of Positive Characteristic

Periodic wavelet frames have gained considerable popularity in recent years, primarily due to their substantiated applications in diverse and widespread fields of science and engineering. In this article, we introduce the concept of periodic wavelet frame on local fields of positive characteristic and show that under weaker conditions the periodization of any wavelet frame constructed by the unitary extension principle with dilation factor 𝔭^?1 is a periodic wavelet frame on local fields. Moreover, based on the mixed extension principle and Fourier-based techniques of the wavelet frames, we present an explicit method for a pair of dual periodic wavelet frames on local fields of positive characteristic.     

Local Rankin-Selberg convolutions for : explicit conductor formula

Let be a non-Archimedean local field and , positive integers. For , let and let be an irreducible supercuspidal representation of . Jacquet, Piatetskii-Shapiro and Shalika have defined a local constant to the and an additive character of . This object is of central importance in the study of the local Langlands conjecture. It takes the form

where is an integer. The irreducible supercuspidal representations of have been described explicitly by Bushnell and Kutzko, via induction from open, compact mod centre, subgroups of . This paper gives an explicit formula for in terms of the inducing data for the . It uses, on the one hand, the alternative approach to the local constant due to Shahidi, and, on the other, the general theory of types along with powerful existence theorems for types in , developed by Bushnell and Kutzko.

     

Characterizing Efficient Empirical Estimators for Local Interaction Gibbs Fields

The expectation of a local function on a stationary random field can be estimated from observations in a large window by the empirical estimator, that is, the average of the function over all shifts within the window. Under appropriate conditions, the estimator is consistent and asymptotically normal. Suppose that the field is a Gibbs field with known finite range of interactions but otherwise unknown potential. We show that the empirical estimator is efficient if and only if the function is (equivalent to) a sum of functions each of which depends only on the values of the field on a clique of sites. This revised version was published online in June 2006 with corrections to the Cover Date.     

Fields with Exceptional Tangent Fields

The asymptotic self-similarity property describes the local structure of a random field. In this paper, we introduce a locally asymptotically self-similar second order field X_H, whose local structures at x=0 and at x0 are very far from each other. More precisely, whereas its tangent field at x0 is a Fractional Brownian Motion, its tangent field at x=0 is a Fractional Stable Motion. In addition, X_H, is asymptotically self-similar at infinity with a Gaussian field, which is not a Fractional Brownian Motion, as tangent field. Then, its trajectories regularity is studied. Finally, the Hausdorff dimension of its graphs is given.