摘要
在核密度函数有足够高阶导数的连续函数类 (而不必在相应 H lder函数类 )中 ,以非整数阶高阶奇异积分和单侧高阶奇异积分的概念为基础 ,以非整数阶高阶奇异积分的微分公式作工具 ,运用降阶法和归纳法 。
When kernal density f(t,τ) is in the class of continuous function to possessing sufficient derivative of high order (and needn't in the class of corresponding Holder finction),on based of the concepts to singular integral of high non\|integral order and one\|side singular integral of high non\|integral order,using the tools with the differential formulas for singular integrals of high non\|integral order,applying method of reducting order and method of induction,in this paper we give the following formulas to changing order of integration for singular integrals of high non\|integral order:∫ L d τ(τ-t 0) n+γ ∫ Lf(t,τ) d t(t-t 1) m+δ =∫ L d t(t-t 1) m+δ ∫ Lf(t,τ) d τ(τ-t 0) n+γ ∫ L d τ(τ-t 0) n+γ ∫ Lf(t,τ) d t(t-τ) m+δ =∫ L d t ∫ Lf(t,τ) d τ(τ-t 0) n+γ (t-τ) m+δ where L is a arc\|wise smooth curve (closed or open) oriented positively, m,n are non\|negative integral, γ=α+ i β≠0,0≤α<1,δ=μ+iν≠0,0≤μ<1,t 0,t 1∈L(t 0,t 1 may be coincident point). In the above formulas the all multivalued functions are taken the determinats branch on L .
出处
《武汉大学学报（自然科学版）》
CSCD
2000年第3期261-265,共5页
Journal of Wuhan University(Natural Science Edition)
基金
国家教委博士点基金!(980 48627)
国家自然科学基金!(199710 64)
武汉大学自强创新科研基金资助项目
关键词
非整数阶高阶奇异积分
换序公式
降阶法
singular integral of high non-integral order
formala for changing order of integration
one-side singular integral of high order
