Status | 已發表Published |
Herglotz’s theorem and quaternion series of positive term | |
Kou, K. I.; Liu, M.; Tao, S. | |
2016-05-10 | |
Source Publication | Mathematical Methods in the Applied Sciences |
ISSN | 1099-1476 |
Pages | 1099-1476 |
Abstract | The present paper first introduces the notion of quaternion infinite series of positive term and establishes its several tests. Next,we give the definitions of the positive-definite quaternion sequence and the positive semi-definite quaternion function, and we extend the classical Herglotz’s theorem to the quaternion linear canonical transform setting. Then we investigate the properties of the two-sided quaternion linear canonical transform, such as time shift characteristics and differential characteristics. Finally, we derive its several basic properties of the quaternion linear canonical transform of a probability measure, in particular, and establish the Bochner–Minlos theorem. |
Keyword | the quaternion infinite series of positive term the positive-definite quaternion sequence the positive-definite quaternion function Herglotz’s theorem the (two-sided) quaternion linear canonical |
Language | 英語English |
The Source to Article | PB_Publication |
PUB ID | 23399 |
Document Type | Journal article |
Collection | University of Macau |
Corresponding Author | Liu, M. |
Recommended Citation GB/T 7714 | Kou, K. I.,Liu, M.,Tao, S.. Herglotz’s theorem and quaternion series of positive term[J]. Mathematical Methods in the Applied Sciences, 2016, 1099-1476. |
APA | Kou, K. I.., Liu, M.., & Tao, S. (2016). Herglotz’s theorem and quaternion series of positive term. Mathematical Methods in the Applied Sciences, 1099-1476. |
MLA | Kou, K. I.,et al."Herglotz’s theorem and quaternion series of positive term".Mathematical Methods in the Applied Sciences (2016):1099-1476. |
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