Share This Article:

Characterization of Periodic Eigenfunctions of the Fourier Transform Operator

Full-Text HTML Download Download as PDF (Size:635KB) PP. 304-312
DOI: 10.4236/ajcm.2013.34040    4,413 Downloads   6,454 Views  

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.


Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

C. Souza and D. Kammler, "Characterization of Periodic Eigenfunctions of the Fourier Transform Operator," American Journal of Computational Mathematics, Vol. 3 No. 4, 2013, pp. 304-312. doi: 10.4236/ajcm.2013.34040.

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.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.