Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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ON FUNCTIONS DEFINED BY ITS FOURIER TRANSFORM

  • 투고 : 2011.11.20
  • 심사 : 2012.01.25
  • 발행 : 2012.05.30
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초록

Fourier transform is well known for trigonometric systems. It is also a very useful tool for the construction of wavelets. The method of constructing wavelets has evolved as times went by. We review some methods. Then we do some calculations on wavelets defined by its Fourier transform.

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참고문헌

  1. C. K. Chui, An introduction to Wavelets, Academic Press, New York, 1992.
  2. David K. Ruch, Patrick J. Van Fleet, Gibbs' phenomenon fo nonnegative compactly supported scaling vectors, J. Math. Anal. Appl. 304(2005), 370-382. https://doi.org/10.1016/j.jmaa.2004.09.030
  3. J. Foster and F. B. Richard, A Gibbs phenomenon for piecewise linear approximation, The Am. Math. Month (1991), 47-49.
  4. J. W. Gibbs, Letter to the editor, Nature 59 (1899), 606.
  5. J. Geronimo, D. Harding, P. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78(1994) 373-401. https://doi.org/10.1006/jath.1994.1085
  6. S.S.Goh, Q. Jiang, T. Xia, Construction of biorthogonal multiwavelets using the lifting scheme, Appl. Comput. Harmon. Aanl. 9(2000) 336-352. https://doi.org/10.1006/acha.2000.0318
  7. A. H. Zemanian, Distribution Theory and Transform Analysis, Dover Publications, INC., New York,1965.
  8. C. Karakis (1998), Gibbs phenomenon in wavelets analysis, Results Math., 34, 330-341. https://doi.org/10.1007/BF03322059
  9. S. Kelly, Gibbs' phenomenon for wavelets, App. Comp. Harmon. Anal 3 (1996).
  10. Lemarie, P.-G., and Meyer, Y., Ondelettes et bases Hilbertinennes, Rev. Mat Iberoamericana 2, 1-18 (1986).
  11. Landau. H.J. and Pollak. H.O (1961), Landau. H.J. and Pollak. H.O (1961), Prolate spheroidal wave functions, Fourier analysis and uncertainty, II, Bell System Tech. J., 40. 65-84 https://doi.org/10.1002/j.1538-7305.1961.tb03977.x
  12. Landau. H.J. and Pollak. H.O (1962), Prolate spheroidal wave functions, Fourier analysis and uncertainty, II, Bell System Tech. J., 41, 65-84.
  13. F. B. Richard, A Gibbs' phenomenon for spline functions, J. Approx. Theory 66 (1996), 334-351.
  14. Slepian. D. and Pollak, H. O. (1961), Prolate spheroidal wave functions, Fourier analysis and uncertainty, I, Bell System Tech. J., 40. 43-64 https://doi.org/10.1002/j.1538-7305.1961.tb03976.x
  15. Slepian, D (1964), Prolate spheroidal wave functions, Fourier analysis and uncertainty, IV, Bell System Tech. J., 43. 3009-3058. https://doi.org/10.1002/j.1538-7305.1964.tb01037.x
  16. Slepian, D (1983), Some comments on Fourier analysis, uncertainty and modelling, SIAM Review, 25. 379-393. https://doi.org/10.1137/1025078
  17. H. T. Shim and H. Volkmer (1996), On Gibbs phenomenon for wavelet expansions, J. Approx. Th., 84, 74-95. https://doi.org/10.1006/jath.1996.0006
  18. L. Villemoes, Energy moments in time and frequency for two scale difference equation solutions and wavelets, SIAM J. Math. Anal., 23(1992), pp. 1519-1543. https://doi.org/10.1137/0523085
  19. G. G. Walter, Wavelets and other orthogonal systems with Applications, CRC Press, Boca Raton, FL., 1994.
  20. G. G. Walter, Wavelets based on prolate spheroidal wave functions, J. of Fourier Anal. and Appal., Vol 10 (1), 2004.