Spectra of a class of self-affine measures

In the present paper we will study the spectral property of a class of self-affine measures under the condition of compatible pair. We first answer a question of Dutkay and Jorgensen concerning the relationship between spectral self-affine measure and compatible pair. We then consider the spectra of Bernoulli convolutions and obtain a sharp result which extends the corresponding result of Jorgensen, Kornelson and Shuman. Finally, we provide a structural property for the integer spectrum of a spectral self-affine measure.     

卷积算子的Gibbs现象

本文建立了一般卷积算子在函数的第一类间断点处有Gibbs现象的刻画定理,并且给出了某些例子.     

Error analysis of large-time approximations for decay chains

Consider a radioactive decay chain X₁ → ? → X_n→ and let N_n(t) be the amount of X_n at time t. This paper establishes error bounds for large-time approximations to N_n(t) that include and generalize the transient equilibrium approximations and other known approximations. The error bounds allow one to find the range of t for which these approximations can be used with a given degree of precision.     

Some applications of Banach algebra techniques

We consider some functional Banach algebras with multiplications as the usual convolution product * and the so‐called Duhamel product ?. We study the structure of generators of the Banach algebras (C⁽ⁿ⁾[0, 1], *) and (C⁽ⁿ⁾[0, 1], ?). We also use the Banach algebra techniques in the calculation of spectral multiplicities and extended eigenvectors of some operators. Moreover, we give in terms of extended eigenvectors a new characterization of a special class of composition operators acting in the Lebesgue space L^p[0, 1] by the formula (C_φf)(x) = f(φ(x)).     

Strongly singular convolution operators on the weighted Herz-type Hardy spaces

Let 0<p≤1<q<0, andw ₁ ,w ₂ ∈ A ₁ (Muckenhoupt-class). In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spacesH K^{α, p} _q(w₁; w₂) to the homogeneous weighted Herz spacesK ^{α, p} _q (w₁; w₂), provided α=n(1−1/q). Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spacesH K ^{α, p} _q (w ₁;w ₂) is also investigated. Supported by the National Natural Science Foundation of China     

关于Montgomery的一个问题

本文解决了Ｍｏｎｔｇｏｍｅｒｙ提出的一个问题．     

Multiplier theorems for special Hermite expansions on Cn

The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderón-Zygmund decomposition. Then the multiplier theorem in Lp(1相似文献   

A discrete algorithm for complex frequency-domain convolutions

ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅＬａｐｌａｃｅｔｒａｎｓｆｏｒｍｏｆｔｈｅｐｒｏｄｕｃｔｏｆｔｗｏｔｉｍｅ＿ｄｏｍａｉｎｓｉｇｎａｌｓｅｑｕａｌｓｔｈｅｃｏｍｐｌｅｘｆｒｅｑｕｅｎｃｙ＿ｄｏｍａｉｎｃｏｎｖｏｌｕｔｉｏｎｏｆｉｎｄｉｖｉｄｕａｌＬａｐｌａｃｅｔｒａｎｓｆｏｒｍｓｏｆｔｗｏｓｉｇｎａｌｓ.Ｇｅｎｅｒａｌｌｙ,ｔｈｅｃｏｎｖｏｌｕｔｉｏｎｏｆｔｗｏｃｏｍｐｌｅｘｆｒｅｑｕｅｎｃｙ＿ｄｏｍａｉｎａｎａｌｙｔｉｃａｌｆｕｎｃｔｉｏｎｓｉｓｃａｌｃｕｌａｔｅ…     

Asymptotic stability of traveling waves in a discrete convolution model for phase transitions

In a recent paper [P. Bates, A. Chmaj, A discrete convolution model for phase transition, Arch. Rational Mech. Anal. 150 (1999) 281-305], a discrete convolution model for Ising-like phase transition has been derived, and the existence, uniqueness of traveling waves and stability of stationary solution have been studied. This nonlocal model describes l₂-gradient flow for a Helmholts free energy functional with general range interaction. In this paper, by using the comparison principle and the squeezing technique, we prove that the traveling wavefronts with nonzero speed is globally asymptotic stable with phase shift.     

The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel

The $z$-transform is introduced to analyze a full discretization method for a partial integro-differential equation (PIDE) with a weakly singular kernel. In this method, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule is considered. The global stability and convergence properties of complete discretization are derived and numerical experiments are reported.