On the Characterization of the Fourier Spectra of Functions Defined on an Abelian Group

Xiao Guozhen

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On the Characterization of the Fourier Spectra of Functions Defined on an Abelian Group

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- On the Characterization of the Fourier Spectra of Functions Defined on an Abelian Group
- Acta Electronica Sinica Issue 7, Pages: 36-42(1992)
- 作者机构：
  
  1.   西安电子科技大学信息保密研究所
  2.   Dept.of Computer Science Dortmund University Dortmund 50  ,4600
  3.   Germany 西安 710071
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：1992
- 稿件说明：
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[1]肖国镇,Claudio Morage.阿贝尔群上函数的傅里叶谱特征[J].电子学报,1992(07):36-42.

Xiao Guozhen. On the Characterization of the Fourier Spectra of Functions Defined on an Abelian Group[J]. Acta Electronica Sinica, 1992, (7): 36-42.
[1]肖国镇,Claudio Morage.阿贝尔群上函数的傅里叶谱特征[J].电子学报,1992(07):36-42. DOI：

Xiao Guozhen. On the Characterization of the Fourier Spectra of Functions Defined on an Abelian Group[J]. Acta Electronica Sinica, 1992, (7): 36-42. DOI：

摘要

本文解决了阿贝尔群上调和分析的如下经典问题:一组有序复数是G

到D中的函敦f的付里叶谱的充分必要条件是甚么?这里D表示（?）（复数域）

（?）（实数域）或G（有限阿贝尔群）。对子G=（?）

的情形

已有的一些结论是本文主要定理的推论。

Abstract

In this paper we solve the following classical problem of Harmonie Analysis on Abelian Groups. Which are the necessary and sufficient conditions that should be satisfied by an ordered set of complex numbers in order to be the Fourier-（Chrestenson）-Spectrum of a function

f: Gnf33D where D may denote

or G? We obtain as corollaries to the main theorems some known results for G = 2

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