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ω-超广义函数空间的结构与关系 被引量：1

Structures and Relations of ω-Ultradistributions
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摘要 讨论了广义函数理论研究中的ω-超广义函数空间的结构和关系.通过Fourier-Lapalace变换建立了ω-超可微函数和ω-超广义函数空间与某些实解析函数空间之间的拓扑同构对应关系,从而可以利用实解析函数空间来考察ω-超可微函数和ω-超广义函数空间的结构和特性.此外,还给出了两类ω-超广义函数的某种结构表示. The structures and relations of ω-ultradistributions in the theory of distributions were dis-cussed.Some topological isomorphism relations between ω-ultra-differentiable functions,ω-ultradistri-butions and some real-analytic function spaces were set up by Fourier-Laplace transform,so that the structures and properties of ω-ultradistributions and ω-ultra-differentiable function spaces could be studied by real-analytic function spaces.Moreover,a structure of two ω-ultradistributions was ob-tained.
作者 薛琳
机构地区 洛阳师范学院数学科学学院
出处 《中北大学学报（自然科学版）》 CAS 北大核心 2015年第2期126-130,共5页 Journal of North University of China(Natural Science Edition)
基金 山西省回国留学人员科研资助项目(2012-011)
关键词 权函数 ω-超可微函数 ω-超广义函数 实解析函数空间 weight functions ω-ultra-differentiable functions ω-ultradistributions real-analytic function spaces
分类号 O177.4 [理学—基础数学]
  • 相关文献

参考文献12

  • 1Boner J, Braun RW, Meise R, et al. Whitney's exten- sion theorem for non-quasianalytic classes of ultradif- ferentiab[ functions[J]. Studia Math. , 1991, 99(2) 155-184.
  • 2Bonet J, Fern/eute{ a} ndez C, Meise R. Characteriza- tion of the w-hypoelliptic convolution opertiors on ul- tradistributions[J]. Ann. Aead. Sci. Fenn. Math., 2000, 25: 261-284.
  • 3Bonet J, Meise R. Ultradistributions of Beurling type and projective descriptions[J]. J. Math. Anal. and AppL , 2001, 255: 122-136.
  • 4Bonet J, Meise R. Quasianalytic functional and projec tive descriptions[J]. Math. Scand. , 2004. 94: 249- 266.
  • 5Braun RW, Meise R, Taylor B A. Ultradifferenfiable functions and Fourier analysis[J]. Resulte Math., 1990, 17: 206-237.
  • 6HOrmander L. Between distributions and hyperfunc tions[J]. Asterisque, 1985, 131. 89-106.
  • 7Meise R, Taylor B A. Whitneys extension theorem for ultradifferentiable functions of Beurling type[J]. Ark. Math. , 1988, 26: 265-287.
  • 8Heinrich T, Meise R. A support theorem for quasiana lytic functionals[J]. Math. Nachr., 2007, 28: 364- 387.
  • 9Braun R W, Meise R, Taylor B A. A characterization of the algebraic surfaces on which the classical Phragm6n-I,indel0f of theorem holds using branch curves[J]. Pure Appl. Math. Q., 2011, 7(1): 139- 197.
  • 10Bonet J, Meise R. On the theorem of Borel for quasi analytic elasses[J]. Math. Scand. , 2013, 112 (2) 302-319.

二级参考文献9

  • 1Bonet J, Braun R W, Meise R, et al. Whitney's exten- sion theorem for non-quasianalytie classes of ultradifferen- tiablfunetions[J]. Studia Math., 1991, 99(2): 155- 184.
  • 2Bonet J, Fernandez C, Meise R. Characterization of the w-hypoelliptic convolution opertiors on ultradistributions [J]. Ann. Acad. Sci. Fenn. Math., 2000, 25: 261- 284.
  • 3Bonet J, Meise R. Ultradistributions of Beurling type and projective descriptions[J]. J. Math. Anal. and Appl. , 2001, 255: 122-136.
  • 4Bonet J, Meise R. Quasianalytic functional and projective descriptions[J]. Math. Scand. , 2004, 94~ 249-266.
  • 5Braun R W, Meise R, Taylor B A. Ultradifferentiable functions and Fourier analysis[J]. Resulte Math. , 1990, 17 : 206-237.
  • 6Hormander L. Cetween distributions and hyperfunctions [J]. Asterisque, 1985, 131: 89-106.
  • 7Meise R, Taylor B A. Whitney' s extension theorem for ultradifferentiable functions of Beurling type [ J ]. Ark. Math., 1988, 26: 265-287.
  • 8Schapira P. Theorie des Hyperfonctions [ M ]. Springer LNM, 1970: 126.
  • 9Heinrich T, Meise R. A support theorem for Quasiana- lyric functionals [J ]. Math. Nachr. , 2007, 28. 364- 387.

共引文献1

同被引文献11

  • 1BonetJ, Braun R W, Meise R, et al. Whitney's extension theorem for non-quasianalytic classes of ultradifferentiabl functions[J]. Studia Math., 1991, 99 (2): 155-184.
  • 2BonetJ, Fernandez C, Meise R Characterization of the or hypoelliptic convolution opertiors on ultradistributions[J]. Ann. Acad. Sci. Fenn. Math., 2000 (25): 261-284.
  • 3BonetJ, Meise R Ultradistributions of Beurling type and projective descriptions[J].J. Math. Anal. and Appl. , 2001(255): 122-136.
  • 4BonetJ, Meise R Quasianalytic functional and projective descriptions[J]. Math. Scand., 2004(94): 249- 266.
  • 5Braun R W, Meise R, Taylor B A A characterization of the algebraic surfaces on which the classical Phragmen-L ind elof of theorem holds using branch curvesDJ. Pure Appl, Math. Q., 2011, 7(1): 139- 197.
  • 6Braun R W, Meise R, Taylor B A Ultradifferentiable functions and Fourier analysis[J]. Resulte Math. , 1990(17): 206-237.
  • 7Hormander L. Between distributions and hyperfunctionsD]. Asterisque , 1985(131): 89-106.
  • 8Meise R, Taylor B. A Whitney's extension theorem for ultradifferentiable functions of Beurling type[J]. Ark. Math. , 1988(26): 265-287.
  • 9Heinrich T, Meise R A support theorem for Quasianalytic Iunctionals[J]. Math. Nachr., 2007 (28): 364- 387.
  • 10BonetJ, Meise R On the theorem of Borel for quasianalytic classes[J]. Math. Scand., 2013, 112 (2): 302-319.

引证文献1

中北大学学报（自然科学版）
2015年 第2期

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