About: Babenko–Beckner inequality

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In mathematics, the Babenko–Beckner inequality (after K. Ivan Babenko and William E. Beckner) is a sharpened form of the Hausdorff–Young inequality having applications to uncertainty principles in the Fourier analysis of Lp spaces. The (q, p)-norm of the n-dimensional Fourier transform is defined to be In 1961, Babenko found this norm for even integer values of q. Finally, in 1975, using Hermite functions as eigenfunctions of the Fourier transform, Beckner proved that the value of this norm for all is Thus we have the Babenko–Beckner inequality that then we have or more simply

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  • In mathematics, the Babenko–Beckner inequality (after K. Ivan Babenko and William E. Beckner) is a sharpened form of the Hausdorff–Young inequality having applications to uncertainty principles in the Fourier analysis of Lp spaces. The (q, p)-norm of the n-dimensional Fourier transform is defined to be In 1961, Babenko found this norm for even integer values of q. Finally, in 1975, using Hermite functions as eigenfunctions of the Fourier transform, Beckner proved that the value of this norm for all is Thus we have the Babenko–Beckner inequality that To write this out explicitly, (in the case of one dimension,) if the Fourier transform is normalized so that then we have or more simply (en)
  • 수학에서, 바벤코-베크너 부등식 (K.Ivan Babenko 및 William E.Beckner의 이름을 따서 지어짐)은 하우스도르프-영 부등식의 더 정확한 형태 중 하나이다. (ko)
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  • 수학에서, 바벤코-베크너 부등식 (K.Ivan Babenko 및 William E.Beckner의 이름을 따서 지어짐)은 하우스도르프-영 부등식의 더 정확한 형태 중 하나이다. (ko)
  • In mathematics, the Babenko–Beckner inequality (after K. Ivan Babenko and William E. Beckner) is a sharpened form of the Hausdorff–Young inequality having applications to uncertainty principles in the Fourier analysis of Lp spaces. The (q, p)-norm of the n-dimensional Fourier transform is defined to be In 1961, Babenko found this norm for even integer values of q. Finally, in 1975, using Hermite functions as eigenfunctions of the Fourier transform, Beckner proved that the value of this norm for all is Thus we have the Babenko–Beckner inequality that then we have or more simply (en)
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  • Babenko–Beckner inequality (en)
  • 바벤코-베크너 부등식 (ko)
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