DOI QR코드

DOI QR Code

A REVERSE OF THE CAUCHY-BUNYAKOVSKY-SCHWARZ INTEGRAL INEQUALITY FOR COMPLEX-VALUED FUNCTIONS AND APPLICATIONS FOR FOURIER TRANSFORM

  • DRAGOMIR S. S. (SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS, VICTORIA UNIVERSITY OF TECHNOLOGY) ;
  • HANNA G. (SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS, VICTORIA UNIVERSITY OF TECHNOLOGY) ;
  • ROUMELIOTIS J. (SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS, VICTORIA UNIVERSITY OF TECHNOLOGY)
  • Published : 2005.11.01

Abstract

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

References

  1. E. O. Brigham, The Fast Fourier Transform and its Applications, Englewood Cliffs, NJ: Prentice-Hall Inc., 1988
  2. N. S. Barnett and S. S. Dragomir, An approximation for the Fourier transform of absolutely continuous mappings, Proc. 4th Int. Conf. on Modelling and Simulation, Victoria University, Melbourne, 2002, 351-355. RGMIA Res. Rep. Coll. 5 (2002), Supplement, Article 33. [ONLINE: http://rgmia.vu.edu.au/v5(E).html]
  3. N. S. Barnett, S. S. Dragomir, and G. Hanna, Error estimates for approximating the Fourier transform of functions of bounded variation, RGMIA Res. Rep. Coll. 7 (2004), no, 1, Articla 11. [ONLINE: http://rgmia.vu.edu.au/v7n1.html]
  4. S. S. Dragomir, Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces, RGMIA Res. Rep. Coll. 6 (2003), Supplement, Article 19, [ONLINE: http://rgmia.vu.edu.au/v6(E).html].
  5. S. S. Dragomir, Y. J. Cho, and S. S. Kim, An approximation for the Fourier transform of Lebesgue integrable mappings, in Fixed Point Theory and Applications, Vol. 4, Y. J. Cho, J. K. Kim, and S. M. Kong (Eds.), Nova Science Publishers Inc., 2003, pp. 67-74
  6. W. Greub and W. Rheinboldt, On a generalisation of an inequality of L. V. Kantorovich, Proc. Amer. Math. Soc. 10 (1959), 407-415
  7. G. Polya and G. Szego, Aufgaben und Lehrsatze aus der Analysis, Vol. 1, Berlin 1925, pp. 57 and 213-214
  8. G. S. Watson, Serial correlation in regression analysis I, Biometrika 42 (1955), 327-342 https://doi.org/10.1093/biomet/42.3-4.327

Cited by

  1. Reverses of Schwarz inequality in inner product spaces with applications vol.288, pp.7, 2015, https://doi.org/10.1002/mana.201300100
  2. An additive reverse of the Cauchy–Bunyakovsky–Schwarz integral inequality vol.21, pp.4, 2008, https://doi.org/10.1016/j.aml.2007.05.011