Abstract
In this paper, Hardy’s theorem and rotations characterized by complex Gaussians in the complex plane due to Hogan and Lakey are extended to complex spaces of several variables. We point out that conditions under which a function on the n-dimensional real Euclidean space has an analytic extension to the complex space. Moreover, we prove that the function is a rotation of a multiple of real Gaussians through some angle if the extension satisfies certain assumptions.
Реэюме
В данной работе даются сарактеризации теоремы Харди и вращений в комплексной плоскости по Согану и Лэйки, и комплексные Тауссианы распространяются на случай комплексного пространства в нескольких переменныс. Приводятся условия, при выполнении которых функция на n-мерном вещественном Евклндовом пространстве имеет аналитическое продолжение на комплексное пространство. Более того, мы устанавливаем, что эта функция естъ вращение многомерного веЩественного Гауссиана на некооопый угол, если продолжение удовлетворяет некоторым условиям.
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The project supported by the China National Natural Science Foundation (Program No. 10871157) and Specialized Research Fund for the Doctoral Program of Higher Education (Program No. 200806990032).
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Tang, S., Niu, P. Hardy’s theorem and rotations of several complex variables. Anal Math 35, 273–287 (2009). https://doi.org/10.1007/s10476-009-0403-y
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DOI: https://doi.org/10.1007/s10476-009-0403-y