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 Herglotz's theorem and quaternion series of positive term Kou K.I.2 ; Liu M.-S.2; Tao S.-Z.2 2016-12-01 Source Publication Mathematical Methods in the Applied Sciences ISSN 10991476 01704214 Volume 39Issue:18Pages:5607-5618 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. Copyright © 2016 John Wiley & Sons, Ltd. Keyword Herglotz's Theorem The (Two-sided) Quaternion Linear Canonical Transform The Positive-definite Quaternion Function The Positive-definite Quaternion Sequence The Quaternion Infinite Series Of Positive Term DOI 10.1002/mma.3945 URL View the original Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000388308500037 全文获取链接 引用统计 Document Type Journal article 专题 DEPARTMENT OF MATHEMATICS Affiliation 1.Universidade de Macau2.South China Normal University 推荐引用方式GB/T 7714 Kou K.I.,Liu M.-S.,Tao S.-Z.. Herglotz's theorem and quaternion series of positive term[J]. Mathematical Methods in the Applied Sciences,2016,39(18):5607-5618. APA Kou K.I.,Liu M.-S.,&Tao S.-Z..(2016).Herglotz's theorem and quaternion series of positive term.Mathematical Methods in the Applied Sciences,39(18),5607-5618. MLA Kou K.I.,et al."Herglotz's theorem and quaternion series of positive term".Mathematical Methods in the Applied Sciences 39.18(2016):5607-5618.
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