Analysis Mathematica

, Volume 10, Issue 4, pp 301–310 | Cite as

Spectral orders and convolution

  • Yūji Sakai


Spectral Order 
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Спектральные порядк и и свертка


Известное неравенст во Ф. Рисса (R) ∝ −∞ −∞ fg(y)h(x−y) dx dy ≦ ∝ −∞ −∞ f^(x)g^(y)h^(x−y)dx dy (f,g≧0) переформулирует ся в терминах отношен ия ≺ частичной упорядоче нности ХардиЛиттлву да—Полиа:f×g≺f^×g^(f,g ≧ 0) где f^ и g^ обозначает с имметрические убыва ющие перестановки функци иf и g соответст-венно, аX — операция сверточ ного произведения. До казано, что операция сверточног о произведения сохран яет отношение частич ного порядка в классе неотрицател ьных симметрич-но убывающих функцийf1f2 тогда и только то гда, когдаf 1 ^ ×g≺f2×g дл я всех 0≦g. Даны дальнейшие обоб щения и некоторые при ложения этих теорем.


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Copyright information

© Akadämiai Kiadó 1984

Authors and Affiliations

  • Yūji Sakai
    • 1
  1. 1.Department of Applied Mathematics Faculty of EngineeringShinshu UniversityNagano-ShiJapan

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