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- Title
Herglotz's theorem and quaternion series of positive term.
- Authors
Kou, Kit Ian; Liu, Ming ‐ Sheng; Tao, Shu ‐ Zhen
- 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.
- Subjects
QUATERNION functions; MATHEMATICS theorems; INFINITY (Mathematics); INTEGRAL transforms; PROBABILITY theory
- Publication
Mathematical Methods in the Applied Sciences, 2016, Vol 39, Issue 18, p5607
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.3945