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Original Articles

Some Localization Properties of the Lp Continuous Wavelet Transform

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Pages 87-99 | Received 08 Mar 2017, Accepted 10 Jul 2017, Published online: 15 Sep 2017

References

  • W. Beckner (1975). Inequalities in Fourier analysis. Ann. Math. 102(1):159–182.
  • M. Benedicks (1985). On the fourier transform of functions supported on sets of finite lebesgue measure. J. Math. Anal. Appl. 106(1):180–183.
  • M. G. Cowling and J. F. Price (1984). Bandwidth versus time concentration: The Heisenberg-Pauli-Weyl inequality. SIAM J. Math. Anal. 15(1):151–165.
  • S. Dahlke and P. Maass (1995). He affine uncertainty principle in one and two dimensions. Comput. Math. Appl. 30(3):293–305.
  • P. Dang, G. T. Dang, and T. Qian (2013). A tighter uncertainty principle for the linear canonical transform in terms of phase derivative. IEEE Trans. Signal Proc. 61(21):5153–5164.
  • E. Wilczok (2000). New uncertainty principles for the continuous Gabor transform and the continuous wavelet transform. Docum. Math. 5:201–226.
  • L. Grafakos (2004). Classic and Modern Fourier Analysis. Pearson. New Jersey, USA.
  • K. Gröchenig (1996). An uncertainty principle related to the poisson summation formula. Studia Math. 121(1):87–104.
  • K. Gröchenig (2001). Foundations of Time-Frequency Analysis. Birkhäuser. New York, USA.
  • A. Grossman and J. Morlet (1984). Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal. 15(4):721–736.
  • A. J. E. M. Janssen (1998). Proof of a conjecture on the supports of Wigner distributions. J. Fourier Anal. Appl. 6:723–726.
  • P. Korn (2005). Some uncertainty principles for time-frequency transforms of the cohen class. IEEE Trans. Signal Proc. 53(2):523–527.
  • S. K. Sharma and D. Joshi (2008). Uncertainty principle for real signals in the linear canonical transforms domains. IEEE Trans. Signal Proc. 56(7):2677–2683.
  • P. J. Loughlin and L. Cohen (2004). The uncertainty principle: Global, local or both? IEEE Trans. Signal Proc. 53(5):1218–1227.
  • S. Mallat (2008). A Wavelet Tour of Signal Processing. Academic Press. Burlington MA, USA.
  • V. Perrier and C. Basdevant (1996). Besov norms in terms of the continuous wavelet transform. Application to structure functions. Math. Models Methods Appl. Sci. 6(5):649–664.
  • J. F. Price (1983). Inequalities and local uncertainty principles. J. Math. Phys. 24:1711–1714.
  • J. F. Price (1987). Sharp local uncertainty principles. Studia Math. 85(1):37–45.
  • J. F. Price and A. Sitaram (1988). Functions and their Fourier transforms with supports of finite measure for certain locally compact groups. J. Funct. Anal. 79(1):166–188.
  • C. Sagiv, N. A. Sochen, and Y. Y. Zeevi (2006). The uncertainty principle: Group theoretic approach, possible minimizers and scale-space properties. J. Math. Imaging Vis. 26(1–2):149–166.
  • P. Singer (1999). Uncertainty inequalities for the continuous wavelet transform. IEEE Trans. Inf. Theory 45(3):1039–1042.
  • A. Torchinsky (1986). Real Variable Methods in Harmonic Analysis. Dover. Academic Press, London, UK.
  • A. Zygmund and R. I. Wheeden (1977). Measure and Integral: An Introduction to Real Analysis. Chapman and Hall-CRC. New York, USA.
  • Y. L. Li, J. Zhao, and R. Tao (2009). Uncertainty principles for linear canonical transform. IEEE Trans. Signal Proc. 57(7):2856–2858.

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