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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 PublicationMathematical Methods in the Applied Sciences
ISSN10991476 01704214
Volume39Issue: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.

KeywordHerglotz'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
DOI10.1002/mma.3945
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000388308500037
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Document TypeJournal article
专题DEPARTMENT OF MATHEMATICS
Affiliation1.Universidade de Macau
2.South China Normal University
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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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