relatingfourierhyperfunctionsandextendedfourierhyperfunctiontohermiteheatequation

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	relatingfourierhyperfunctionsandextendedfourierhyperfunctiontohermiteheatequation
	LI BangHe
	2006
发表期刊	应用泛函分析学报
ISSN	1009-1327
卷号	8 期号:4 页码:295
摘要	It was proved by K.W. Kim, S.Y. Chung and D. Kim that if a C~∞-solution u(x,t) of the heat equation in R~+_(n+1) satisfiesfor any ε＞ 0, and some C ＞ 0, then its boundary determines a unique Fourier hyperfunction; and conversely, any Fourier hyperfunction is the boundary of such a u(x. t). Also, S. Y. Chung, D. Kim and K. Kim showed that replacing "any ε＞0" by "some ε＞0", then the above statements are true for extended Fourier hyperfunctions (called Fourier ultra-hyperfunctions also in the literature).We show that replacing solutions of the heat equation by solutions U(x,t) of the Hermite heat equation, and exp then the above results relating Fourier hyperfunctions and extended Fourier hyperfunctions to heat equation become the relations with Hermite heat equations.Furthermore we proved that for fixed t,U(x,t) is an element of the space of test functions for extended Fourier hyperfunctions, thus Fourier hyperfunctions and extended Fourier hyperfunctions are limits of such nice functions. This gives also a new proof of the recent result of K. Kim on denseness of test functions in the space of extended Fourier hyperfunctions. Perhaps, the most interesting thing is that if U(x,t) represents a Fourier hyperfunction or an extended Fourier hyperfunction u, then the Fourier transformation of U(x,t) with respect to x represents the Fourier transformation of u.
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/43176
专题	系统科学研究所
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	LI BangHe. relatingfourierhyperfunctionsandextendedfourierhyperfunctiontohermiteheatequation[J]. 应用泛函分析学报,2006,8(4):295.
APA	LI BangHe.(2006).relatingfourierhyperfunctionsandextendedfourierhyperfunctiontohermiteheatequation.应用泛函分析学报,8(4),295.
MLA	LI BangHe."relatingfourierhyperfunctionsandextendedfourierhyperfunctiontohermiteheatequation".应用泛函分析学报 8.4(2006):295.