Equality of two spectra arising in harmonic analysis and semigroup theory

We show that a new notion of a spectrum of a function ( is a Banach space), defined by B. Basit and the first author, coincides with the Arveson spectrum of some shift group, provided is uniformly continuous. We apply this result to prove a new version of a tauberian theorem.     

Bent函数的一般构造法

本文用概率方法给出小项表示的布尔函数谱的性质,据此得到了Ｂｅｎｔ函数的特征矩阵的等价刻画,原则上给出了Ｂｅｎｔ函数的一般构造法,并为Ｂｅｎｔ函数的计数问题提供了一个模型。文中还提出了Ｂｅｎｔ矩阵的概念,考察了Ｂｅｎｔ矩阵的性质,并借助Ｂｅｎｔ矩阵得到由已知Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数构造新的Ｂｅｎｔ函数的方法。     

小波包分解及其参数模型

本文在小波包分析的基础之上，实现了适合于一维信号分析的小波分解算法，并将小波包分析理论和参数模型有机地结合了起来，构造了小波包参数模型。     

环状膦酸酯的合成及其质谱特征

本文研究了环状膦酸酯的合成方法，通过三种方法合成了十五个具有各种烷基结构的六元和七元环膦酸酯，并对这十五个化合物质谱作了分析和归纳，得出了一些有助于鉴定这类膦酸酯的质谱特征。     

A note on the spectrum of an upper triangular operator matrix

Let be a upper triangular operator matrix acting on the Banach space . We investigate the set of the operators for which , where denotes the spectrum.

     

Spectra of certain types of polynomials and tiling of integers with translates of finite sets

We investigate Fuglede's spectral set conjecture in the special case when the set in question is a union of finitely many unit intervals in dimension 1. In this case, the conjecture can be reformulated as a statement about multiplicative properties of roots of associated with the set polynomials with (0,1) coefficients. Let be an N-term polynomial. We say that {θ₁,θ₂,…,θ_N−1} is an N-spectrum for A(x) if the θ_j are all distinct and

     

Spectrum of interpolated operators

Let be a compatible pair of Banach spaces and let be an operator that acts boundedly on both and . Let be the corresponding operator on the complex interpolation space .

The aim of this paper is to study the spectral properties of . We show that in general the set-valued function is discontinuous even in inner points and show that each operator satisfies the local uniqueness-of-resolvent condition of Ransford. Further we study connections with the real interpolation method.

     

The spectra of nonnegative integer matrices via formal power series

We characterize the possible nonzero spectra of primitive integer matrices (the integer case of Boyle and Handelman's Spectral Conjecture). Characterizations of nonzero spectra of nonnegative matrices over and follow from this result. For the proof of the main theorem we use polynomial matrices to reduce the problem of realizing a candidate spectrum to factoring the polynomial as a product where the 's are polynomials in satisfying some technical conditions and is a formal power series in . To obtain the factorization, we present a hierarchy of estimates on coefficients of power series of the form to ensure nonpositivity in nonzero degree terms.

     

N2+分子离子A2∏u-X2∑+g 系(2,0)带光外差速度调制光谱

采用光外差速度调制光谱技术研究了N2+分子离子A2∏u-X2∑+g 系(2,0)带转动光谱．由于所用技术的高灵敏度特性，精确地确定了该带310条谱线的频率，其中，那些重叠谱线的频率也通过解谱精确地确定了．利用标准Hamilton量，采用非线性最小二乘方法对该带进行了分析，获得了最精确的分子常数．     

Spectrum of a homogeneous graph

We describe the spectrum of the Laplacian for a homogeneous graph acted on by a discrete group. This follows from a more general result which describes the spectrum of a convolution operator on a homogeneous space of a locally compact group. We also prove a version of Harnack inequality for a Schrödinger operator on an invariant homogeneous graph.