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超可微函数空间ε＊和D＊中的乘法和卷积运算 被引量：8

Multiplications and Convolutions in Ultradifferentiable Function Spaces ε_* and D_*
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摘要 利用Fourier-Laplace变换对ω-超可微函数空间ε_*(R^N)和ω-试验函数空间D*(R^N)中的乘法和卷积运算进行了讨论,并且证明了D(R^N)是D*(R^N)的乘子空间,在卷积意义下D(R^N)是ε_*(R^N)的乘子空间,且在D*(R^N)中Parseval等式成立. In this paper, the multiplication and convolution of functions in the ω- ultradifferentiable function spaces ε＊（R^N） and ω-test function spaces D＊（R^N） are discussed, and it is obtained that D＊（R^N） is the multiplier space of D＊（R^N）, D（R^N） is the multiplier space of ε＊（R^N） in the sense of convolution, and the Parseval equation holds in the spaces of D＊（R^N）.
作者 王光 李爱枝
机构地区 山西大学数学科学学院 广州大学松田学院基础部
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2008年第1期61-68,共8页 Acta Mathematica Sinica：Chinese Series
基金 山西省自然科学基金(2006011001) 山西省回国人员基金
关键词 加权函数 Fourier-Laplace变换 卷积 weight function Fourier-Laplace transform convolution
分类号 O177.4 [理学—基础数学]
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参考文献17

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同被引文献30

  • 1BRAUN R W, MEISE R, TAYLOR B A. Utradifferentiable functions and Fourier analysis [ J ]. Resuhe Math, 1990 (17) :206- 237.
  • 2MEISE R,TAYLOR B A, VOGT D. Characterization of the linear partial differential operators with constant coefficients that admidt a tinuous linear right inverse [ J ]. Ann. Inst. Fourier( Grenoble), 1990,40:619-655.
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  • 6Bjorck G. Linear partial differential operators and generalized distributions [J]. Ark. Math. , 1965, 6:351 - 407.
  • 7Bonet J, Meise R. Ultradistributions of brurling type and projective descriptions[J]. J. Math. Anal. andAppl, 2001,255:122 - 136.
  • 8Bonet J,Meise R. Quasianalytic functional and projective descriptions[J]. Math. Scand, 2004,94 : 249 - 266.
  • 9Braun RW, Meise R, Taylor B A. Ultradifferentiable functions and Fourier analysis[J]. ResulteMath. , 1990, 17:206 - 237.
  • 10A. Beurling. Quasi -aualyticity and general distributions[J]. Lectures 4 and 5 ,AMS Summer lustitute, Standford. 1961.

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数学学报（中文版）
2008年 第1期

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