Complete analysis of The Eigen functions of Fourier Transform

机译：完全分析傅里叶变换的eIGEN函数

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In this paper, we proposed an analysis of Eigen functions of the n-Dimensional Fourier transform. We extended the theory developed in our previous publication [1]. We applied our extended theory of systematic construction of Eigen function concept for sine and cosine functions. We explained the concept in a clear way through example construction of Eigen functions of 1-D and 2-D Fourier transform for real even case with negative Eigen value. PP Vaidyanathan discussed in his paper [2] that construction of complex Eigen function f_1+ jf_2 is possible when both functions f_1 and f_2 are either real even or real odd. But he didn't discuss what will happen when f_1 and f_2 are different. We subjected this concept and derived the necessary expressions for complex Eigen functions when function f_1 is even and function f2 is odd vice versa.

机译：在本文中，我们提出了N维傅里叶变换的特征函数的分析。我们扩展了我们以前的出版物[1]的理论。我们应用了我们的统一功能概念的扩展理论，为正弦和余弦功能。我们以明确的方式解释了概念，通过实施例构造了1-D和2-D傅里叶变换的eIGen函数，对于具有负eIGEN值的真实偶数壳体。在他的论文中讨论的PP Vaidyanathan [2]当函数f_1和f_2都是真正的偶数或真实奇数时，可以建造复杂的eIGen函数f_1 + jf_2。但他没有讨论F_1和F_2不同时会发生什么。我们对此概念进行了此概念，当函数f_1是偶数并且函数f2为奇数反之亦然时，为复杂的eIGen函数导出了必要的表达式。

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《ICCCI 2013;International Conference on Computer Communication and Informatics》|2013年||共6页
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Nagendra Prasad Mandru; Durga Prasad Bavirisetti; Yepuganti Karuna; Ravindra Dhuli;
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中图分类 TN919-532;
关键词
Eigen value; Eigen function; real even; real odd; sinusoidal.;

机译：特征值;eIgen函数;真实偶数;真正的奇数;正弦。;

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1. The numerical method of Fourier eigen transform and its application in seismicity analysis [J] . 陈兵, 郑治真, 江在森地震学报：英文版 . 1997,第006期

机译：傅里叶eIGen变换的数值方法及其在地震性分析中的应用
2. Correlation functions of complete CBOC signals derived as the inverse Fourier transform of energy spectra [J] . Yarlykov M. S., Yarlykova S. M. Journal of Communications Technology and Electronics . 2017,第2期

机译：完整CBOC信号的相关函数作为能谱的傅立叶逆变换
3. Fourier transforms in the “classical sense”, Schur spaces and a new formula for the Fourier transforms of slowly increasing, O(p, q)-invariant functions [J] . Norbert Ortner Indagationes Mathematicae . 2013,第1期

机译：“经典意义”上的傅立叶变换，舒尔空间和缓慢增加的O（p，q）不变函数的傅立叶变换的新公式
4. Complete analysis of the Eigen functions of Fourier transform [C] . Mandru Nagendra Prasad, Bavirisetti Durga Prasad, Karuna Yepuganti, 2013 International Conference on Computer Communication and Informatics. . 2013

机译：傅立叶变换的本征函数的完整分析
5. ENTIRE FUNCTIONS AND FOURIER TRANSFORMS. [D] . GHUSAYNI, BADIH NAJIB. 1986

机译：整个功能和傅里叶变换。
6. Functional Roles of D2-Lys317 and the InteractingChloride Ion in the Water Oxidation Reaction of Photosystem II AsRevealed by Fourier Transform Infrared Analysis [O] . Hiroyuki Suzuki, Jianfeng Yu, Takashi Kobayashi, -1

机译：D2-Lys317的功能作用及其相互作用光系统II As的水氧化反应中的氯离子通过傅立叶变换红外分析揭示
7. (with an Author's Supplement on Monotonic Functions, Stieltjes Integrals and Harmonic Analysis). (Translated from the original 1932 German edition by M. Tenenbaum and H. Pollard.)S.BochnerLectures on Fourier Integrals$5.00Annals of Mathematics Study No. 421959Princeton University PressNew York333(reprinted 1953)S.BochnerK.ChandrasekharanFourier Transforms$3.50Annals of Mathematics Study No. 191948Princeton University Press219$4.50S.BochnerHarmonic Analysis and the Theory of Probability1955University of California Press176 [O] . Mandelbrot Benoit 1960

机译：（以及有关单调函数，Stieltjes积分和调和分析的作者补充）。（由M.Tenenbaum和H.Pollard撰写的1932年德文原版翻译而成）S.Bochner傅里叶积分讲义$ 5.00数学研究年鉴421959普林斯顿大学出版社纽约333（再版1953年）S.Bochner K.ChandrasekharanFourier变换$ 3.50数学研究年鉴$ 3.50 No.191948普林斯顿大学出版社219美元4.50 S.Bochner谐波分析与概率论1955年加利福尼亚大学出版社176
8. TABLES FOR THE NUMERICAL DETERMINATION OF THE FOURIER TRANSFORM OF A FUNCTION OF TIME AND THE INVERSE FOURIER TRANSFORM OF A FUNCTION OF FREQUENCY, WITH SOME APPLICATIONS TO OPERATIONAL CALCULUS METHODS [R] . Carl R. Huss, James J. Donegan 1957

机译：用于数值确定时间函数的傅立叶变换和频率函数的逆傅立叶变换的数字表，以及对运算计算方法的一些应用

Complete analysis of The Eigen functions of Fourier Transform

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