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Herglotz’s theorem and quaternion series of positive term
Kou, K. I.; Liu, M.; Tao, S.
2016-05-10
Source PublicationMathematical Methods in the Applied Sciences
ISSN1099-1476
Pages1099-1476
AbstractThe 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.
Keywordthe 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 ArticlePB_Publication
PUB ID23399
Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorLiu, 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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