论文标题
Quaternionic阳性在实际线上的频谱表征
Spectral characterization of quaternionic positive definite functions on the real line
论文作者
论文摘要
本文关注的是Quaternionic阳性在真实线上的频谱特征。我们通过两种不同类型的功能演算将石头定理概括为右Quaternion线性单参数统一组的情况。从广义石的定理中，我们获得了连续的Quaternion阳性确定功能和光谱系统之间的对应关系，即光谱度量的工会和彼此通勤的单一反自我的联合接合操作员；然后推断出连续的四个离子阳性确定函数的傅立叶变换是一种不寻常的季相值措施，可以通过两种不同的方式等效地描述。一个与光谱系统有关（由第一个广义石的定理诱导），另一个与非负有有限的硼孔测量（由第二个广义石的定理诱导）有关。还提出了对弱固定的Quaternion随机过程的应用。
This paper is concerned with the spectral characteristics of quaternionic positive definite functions on the real line. We generalize the Stone's theorem to the case of a right quaternionic linear one-parameter unitary group via two different types of functional calculus. From the generalized Stone's theorems we obtain a correspondence between continuous quaternionic positive definite functions and spectral systems, i.e., unions of a spectral measure and a unitary anti-self-adjoint operator that commute with each other; and then deduce that the Fourier transform of a continuous quaternionic positive definite function is an unusual type of quaternion-valued measure which can be described equivalently in two different ways. One is related to spectral systems (induced by the first generalized Stone's theorem), the other is related to non-negative finite Borel measures (induced by the second generalized Stone's theorem). An application to weakly stationary quaternionic random processes is also presented.
