Dunkl算子的非局部运算演算
Nonlocal Operational Calculi for Dunkl Operators
摘要：
在任意的非局部边值条件下，考虑了一维Dunkl算子$D_k$的非负参数$k$.研究了满足该条件的$D_k$的右逆算子。本文发展了一种Mikusinski型的算子演算。在这种运算演算的框架下，提出了求解Dunkl泛函微分方程$P(D_k)u=f$的非局部Cauchy边值问题的Heaviside算法的一个推广，该方程的多项式为$P$.这些方程的平均周期函数的解决方案减少到这样的问题。得到了平均周期函数存在唯一解的充要条件。
英文摘要：
The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_k)u=f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found.
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