کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4615616 1339323 2015 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An extension of Herglotz's theorem to the quaternions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
An extension of Herglotz's theorem to the quaternions
چکیده انگلیسی

A classical theorem of Herglotz states that a function n↦r(n)n↦r(n) from ZZ into Cs×sCs×s is positive definite if and only if there exists a Cs×sCs×s-valued positive measure μ   on [0,2π][0,2π] such that r(n)=∫02πeintdμ(t) for n∈Zn∈Z. We prove a quaternionic analogue of this result when the function is allowed to have a number of negative squares. A key tool in the argument is the theory of slice hyperholomorphic functions, and the representation of such functions which have a positive real part in the unit ball of the quaternions. We study in great detail the case of positive definite functions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 421, Issue 1, 1 January 2015, Pages 754–778
نویسندگان
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