Characterization of Periodic Eigenfunctions of the Fourier Transform Operator

Comlan de Souza, David W. Kammler

Department of Mathematics, California State University at Fresno, Fresno, USA.
Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, USA.

DOI: 10.4236/ajcm.2013.34040                

Abstract

We generalize this result to p₁,p₂-periodic eigenfunctions of F on R² and to p₁,p₂,p₃-periodic eigenfunctions of F on R³.

Keywords

Eigenfunction; Fourier Transform Operator

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. N. Bracewell, “Fourier Analysis and Imaging,” Kluwer Academic, New York, 2003. http://dx.doi.org/10.1007/978-1-4419-8963-5
[2]	L. Schwartz, “Theorie des Distributions,” Hermann, Paris, 1950.
[3]	R. Strichartz, “A Guide to Distribution Theory and Fourier Transforms,” CRC Press, Inc., Boca Raton, 1994.
[4]	B. Osgood, “The Fourier Transform and Its Applications,” Lecture Notes, Stanford University, 2005.
[5]	D. W. Kammler, “A First Course in Fourier Analysis,” Prentice Hall, New Jersey, 2000.
[6]	J. I. Richards and H. K. Youn, “Theory of Distributions: A Non-technical Introduction,” Cambridge University Press, Cambridge, 1990. http://dx.doi.org/10.1017/CBO9780511623837
[7]	M. J. Lighthill, “An Introduction to Fourier Analysis and Generalized Functions,” Cambridge University Press, New York, 1958. http://dx.doi.org/10.1017/CBO9781139171427
[8]	L. Auslander and R. Tolimieri, “Is Computing with the Finite Fourier Transform Pure or Applied Mathematics?” Bulletin of the American Mathematical Society, Vol. 1, 1979, pp. 847-897. http://dx.doi.org/10.1090/S0273-0979-1979-14686-X
[9]	J. H. McClellan and T. W. Parks, “Eigenvalue and Eigenvector Decomposition of the Discrete Fourier Transform,” IEEE Transactions on Audio and Electroacoustics, Vol. 20, No. 1, 1972, pp. 66-74. http://dx.doi.org/10.1109/TAU.1972.1162342
[10]	M. Senechal, “Quasicrystals and Geometry,” Cambridge University Press, New York, 1995.