加权Stepanov伪概自守函数的一些基本性质及其对Volterra积分方程的应用

本文主要研究加权Stepanov伪概自守函数的一些基本性质.首先,本文研究一个加权Stepanov伪概自守函数与它的Stepanov概自守部分的关系.利用这些关系,本文将这类函数的复合定理进行改进.其次,本文研究加权Stepanov伪概自守函数空间中的卷积算子,这里的卷积算子是由绝对可积函数所生成.最后,应用压缩映射原理,本文得到两类Volterra积分方程的加权Stepanov伪概自守解的存在唯一性.本文的结果推广了部分已知结果.     

单位圆盘加权Bergman空间上Toeplitz算子的本性范数

对于D上的Carleson测度μ而言,本文研究在加权Bergman空间Aα~2（D）上具有符号μ的Toeplitz算子Tμ的一些特殊的性质.近几年,在加权Bergman空间Aα~2（D）上的Toeplitz算子的有界性和紧性已经被广泛研究.为了了解Toeplitz算子Tμ的一些其他性质,本文需要估算出单位圆盘的加权Bergman空间上Toeplitz算子的本性范数的界限.     

加权Fock空间F_α~2上的测不准原理的推广（英文）

对α 0,本文主要研究了复平面上的加权Fock空间F_α~2上的自伴算子和线性算子的测不准原理.利用泛函分析中的一般性原理,在F_α~2上构造了两个线性算子Tf=(f′)/α和T*=zf.进一步,构造了满足条件的两个自伴算子A和B,使得[A,B]为恒等算子的常数倍,得到了F_α~2上更精确的算子的测不准原理形式,其中T*是T的对偶算子,[A,B]=AB-BA为A和B的换位置.本文的结果推广并完善了屈非非和朱克和在文献[1]和[2]中的结果.     

单位球中解析函数Hilbert空间上的加权复合算子的伴随及其应用

主要给出了具有再生核的解析函数Hilbert空间中由任意ψ及Ψ所导出的加权复合算子的对偶算子的一般公式.在此基础上,得到了由一些特殊函数所导出的加权复合算子Cψ,Ψ.的对偶算子的更优美结果.最后还给出了加权Bergman空间中CCψ,Ψ自伴的充要条件.     

单位球上加权Begrman空间和Hardy空间上的保范复合算子

作者证明了复合算子C_φ是单位球上加权Begrman空间上的保范算子当且仅当φ是旋转变换.对单位球上的Hardy空间上的保范复合算子仅得到部分结果.     

三参数区间数集成算子及决策应用

研究了三参数区间数信息集成算子及其在决策中的应用.首先,给出了三参数区间数的有序加权CP-OWA算子、有序加权CP-OWG算子及广义有序加权CP-OWA算子和广义有序加权CP-OWG算子的概念,并初步探讨了它们的性质,推广了相关文献中的三参数区间数加权CP-OWA算子和加权CPOWG算子.然后,通过方案三参数区间数属性值的可能度得到方案属性值可能度矩阵,进而根据可能度矩阵的排序向量实现方案三参数区间数属性值的排序,并通过文中定义的三参数区间数信息集成算子进行信息集成,实现方案排序择优.     

Calderón-Zygmund型算子交换子的加权尖锐估计

本文讨论了θ-型Calderón-Zygmund算子与BMO函数生成的交换子的加权估计.在权函数仅为非负局部可积函数或属于A∞的假设下,当0相似文献   

关于算子加权广义逆的反序律

本文研究了Hilbert空间上两个算子乘积的加权广义逆的反序律.利用算子的分块矩阵表示,获得了两个算子加权广义逆反序律成立的充要条件,所获结果推广了孙文瑜,魏益民和Djordjevic Dragan S.的相关结果.     

Szsz-Mirakjan算子逐点加权同时逼近(英文)

本文研究了Szsz-Mirakjan算子加权同时逼近的问题.利用加权光滑模ω2φλ(f,t)ω,获得了Szsz-Mirakjan算子加权同时逼近的点态结果,推广了已知的结果.     

Szász-Mirakjan算子逐点加权同时逼近

本文研究了Szász-Mirakjan算子加权同时逼近的问题.利用加权光滑模ω2φλ(f,t)u,获得了Szász-Mirakjan算子加权同时逼近的点态结果,推广了已知的结果.     

WEIGHTED AVERAGE OF DIRICHLET KERNELS FOR VILENKIN-LIKE SYSTEM

For Vilenkin-like system, the authors define a new operator H*f := supn |Hnf|, where Hnf is the weighted average for partial sums, and prove that H* is of type (Hp* (Gm), Lp(Gm)) for all 1/2 < p ≤∞. As a consequence, the authors prove the operator S*f := supn |Snf| is of type (p, p) for 1 < p < ∞, where Snf is the n-partial sum.     

Hierarchies of sum rules for squares of spherical Bessel functions

A four-term recurrence relation for squared spherical Bessel functions is shown to yield closed-form expressions for several types of finite weighted sums of these functions. The resulting sum rules, which may contain an arbitrarily large number of terms, are found to constitute three independent hierarchies. Their use leads to an efficient numerical evaluation of these sums.     

A Kuznetsov Formula for Kloosterman Sums on GLn

We prove a Kuznetsov sum formula for Kloosterman sums on GL _n corresponding to the big Bruhat cell. Using this formula, a weighted sum of Kloosterman sums can be expressed in spectral decomposition. A non-trivial estimate of the spectral side might lead to a proof of cancellations in sums of Kloosterman sums on GL _n.     

MAXIMAL INEQUALITY AND COMPLETE CONVERGENCES OF NON-IDENTICALLY DISTRIBUTED NEGATIVELY ASSOCIATED SEQUENCES

A maximal inequality for the partial sum of NA sequence is constructed.By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed.The results obtained extend the results of Liang(1999, 2000).     

Certain weighted averages of generalized Ramanujan sums

We derive certain identities involving various known arithmetical functions and a generalized version of Ramanujan sum. L. Tóth constructed certain weighted averages of Ramanujan sums with various arithmetic functions as weights. We choose a generalization of Ramanujan sum given by E. Cohen and derive the weighted averages corresponding to the versions of the weighted averages established by Tóth.     

基于广义WOWA算子的Pythagorean模糊决策方法

针对Pythagorean模糊信息的决策问题,构建广义Pythagorean模糊信息加权有序加权平均(PF-GWOWA)算子。首先,提出PF-GWOWA算子,并证明Pythagorean模糊广义加权平均(PF-GWA)算子、Pythagorean模糊加权有序加权平均(PF-WOWA)算子与Pythagorean模糊加权平均(PF-WA)算子均为PF-GWOWA算子的特例;其次,根据GWOWA算子属性综合权重计算模型,利用PF-GWOWA算子对信息进行集结;最后,通过算例分析和传统方法对比,说明本文提出方法的合理性与有效性。     

Weighted fusion frame construction via spectral tetris

Fusion frames consist of a sequence of subspaces from a Hilbert space and corresponding positive weights so that the sum of weighted orthogonal projections onto these subspaces is an invertible operator on the space. Given a spectrum for a desired fusion frame operator and dimensions for subspaces, one existing method for creating unit-weight fusion frames with these properties is the flexible and elementary procedure known as spectral tetris. Despite the extensive literature on fusion frames, until now there has been no construction of fusion frames with prescribed weights. In this paper we use spectral tetris to construct more general, arbitrarily weighted fusion frames. Moreover, we provide necessary and sufficient conditions for when a desired fusion frame can be constructed via spectral tetris.     

DISJOINT SUPERCYCLIC WEIGHTED PSEUDO-SHIFTS ON BANACH SEQUENCE SPACES

In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space.The disjoint supercyclic properties of weighted translations on locally compact discrete groups,the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space ?~2(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.     

The index of the spin Dirac operator on the weighted projective space and the reciprocity law of the Fourier-Dedekind sum

The main purpose of this paper is to give a geometric interpretation of the reciprocity law of the Fourier-Dedekind sum given by M. Beck and S. Robins. In fact, the V-index of the spin^c Dirac operator on the weighted projective space is equal to the dimension of the space of all weighted homogeneous polynomials of given degree, and this equality gives precisely the Beck-Robins reciprocity law. In this equality, the Fourier-Dedekind sums appear as the localization terms of the V-index of the spin^c Dirac operators and have a relationship to the eta invariants of lens spaces.     

Disjoint Supercyclic Weighted Shifts

Complementing the existing literature in d-hypercyclicity, we characterize disjoint supercyclicity for a finite family of weighted shift operators. Using this characterization, we answer Question 2 in a recent paper by Bès, Martin and Peris in the negative by constructing examples of disjoint supercyclic weighted shifts whose direct sum operator is hypercyclic, but the same shifts operators fail to be disjoint hypercyclic. We also show the Disjoint Blow-Up/Collapse Property and the Strong Disjoint Blow-Up/Collapse Property for disjoint supercyclicity are equivalent when dealing with a finite family with two or more weighted shifts. However, those weighted shifts operators will never satisfy the Disjoint Supercyclicity Criterion. This provides a sharp distinction between disjoint supercyclicity and supercyclicity for a single operator. We provide a partial answer to disjoint supercyclic version of Question 3 in a recent paper by Salas by showing that we can always select an additional operator to add to an family of d-supercyclic weighted shift operators while maintaining the d-supercyclicity. We also show that, in general, this additional operator cannot be another weighted shift.