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| THE DERIVATIVES AND INTEGRALS OF FRACTIONAL ORDER ON \alpha-ADIC GROUPS |
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Citation： |
Jiang Huikun.THE DERIVATIVES AND INTEGRALS OF FRACTIONAL ORDER ON \alpha-ADIC GROUPS[J].Chinese Annals of Mathematics B,1993,14(4):515~526 |
| Page view： 796
Net amount： 577 |
Authors： |
Jiang Huikun; |
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| Abstract： |
This paper, the author studies fractional derivatives and integrals of fractional order \alpha > 0 for functions in L^r(G_\alpha) and Fourier transform for distributions. Under these definitions, the author obtains the formula $x_y^<\alhpa>(x)=|y|^\alpha X_y(x)$ for characters X_y and $(D^{(\alpha)}f)^{\Gamma}=|\cdot|^\alphaf^{\Gamma}$, discusses the existence of the fractional derivatives of test functions, gives relationships between some function spaces, and proves that the fractional derivatives and the fractional integrals are inverse operations one another. |
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