众所周知，分数次积分算子是调和分析中以偏微分方程为背景的一种重要算子。
It is well-known that fractional integral operator is one of the important operators in harmonic analysis with background of partial differential equations.
摘要通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
与微分算子及其逆算子积分算子作比较，讨论了差分算子及其逆算子(和分)。
In comparison with the differential operator and its inverse - integral operator, the difference operator and its inverse (sum operator) are discussed in this paper.
通过对积分算子谱的估计，作者给出了一阶线性微分差分方程在边值条件下解的存在唯一性定理。
In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition.
用微分算子级数法得到分部积分公式，使一类积分计算变得十分简单。
By using differentiator series method, the formula of partial integration is obtained.
本文利用随机收缩，证明具有随机定义域的非线性随机算子方程组的解的存在与唯一性定理，给出非线性随机积分和微分方程组的某些应用，改进和推广了某些结果。
In this paper, several existence and uniqueness theorems of solutions are proved for the system of nonlinear random operator equations with stochastic domain by using general random contraction.
本文利用随机收缩，证明具有随机定义域的非线性随机算子方程组的解的存在与唯一性定理，给出非线性随机积分和微分方程组的某些应用，改进和推广了某些结果。
In this paper, several existence and uniqueness theorems of solutions are proved for the system of nonlinear random operator equations with stochastic domain by using general random contraction.
应用推荐