发表机构
Indian Institute of Technology (Indian School of Mines)（印度理工学院（印度矿业学院））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造任意阶Mehler-Fock变换，去除参数限制，基于微分算子推导变换公式，并定义平移与卷积算子，证明卷积分解性质。
AI 中文摘要
本文通过借助一个正整数k使得Re(mu+k)>-1/2，去除了Re(mu)>-1/2的限制，构造了任意阶的Mehler-Fock变换MF(mu,k)，并基于微分算子M(mu)N(mu)获得了一些变换公式。此外，我们定义了任意阶的Mehler-Fock平移和卷积算子，并证明了在测试函数空间H(mu)中卷积的分解性质成立。
英文摘要
In this paper, we construct the Mehler-Fock transform of arbitrary order MF(mu,k) by removing the restriction Re(mu) > -1/2 with the help of a positive integer k such that Re(mu+k) > -1/2 and obtain some transformation formulae based on the differential operator M(mu)N(mu). Furthermore, we define the Mehler-Fock translation and convolution operators of arbitrary order and demonstrate that the factorization property for the convolution holds in the test function space H(mu).
