کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894521 1533730 2016 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the inversion of Fueter’s theorem
ترجمه فارسی عنوان
درباره وارونگی قضیه Fueter
کلمات کلیدی
قضیه فوئیت؛ ضرایب فوریه؛ توابع hyperholomorphic برش؛ توابع محوری تک ژنی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی

The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space Rn+1Rn+1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension nn. The present work extends the result to all dimensions nn by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function ff defined in a suitable open set in Rn+1Rn+1, where nn is a positive integer, we can find a slice hyperholomorphic function f→ such that f=Δ(n−1)/2f→. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 108, October 2016, Pages 102–116
نویسندگان
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