Research on Fourier multiplier by operating functions on function spaces

函数空间上函数运算的傅里叶乘子研究

基本信息

批准号：
06804010
负责人：
HATORI Osamu
金额：
$ 0.77万
依托单位：
Niigata University (1995-1996)Tokyo Medical University (1994)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1994
资助国家：
日本
起止时间：
1994 至 1996
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06804010/
关键词：
commutative Banach algebra multiplier operating function function space locally compact abelian group Wiener-Pitt phenomenum L^P-multiplier 極大イデアル空間 locallycompact abelian group regular Banach algebra decomposable operator natural sp

项目摘要

In this research I study Fourier multiplier on locally compact abelian groups G.The maximal ideal space of p-q multplier on a comact abelian group is identified. In particular, I proved that the dual group of G is dense in the maximal ideal space, henceforce naturality of sspectra of p-q multiplier is proved. The operating functions of p-2 multplier is also identified. Let C_0M_p (G) denote the algebra of L^p-multiplier whose Fourier transforms vanish at infinity. I proved that the Apostol algebra coincides with the greatest regular closed subalgebra RegC_0M_p (G) and they are maximal, in a sense, in C_0M_p (G). The proof depends on the general results concerning abstract algebras of continuous functions which are modeled after Fourier multipliers. I also proved that if the maximal ideal space of the algebra in thin, they the greatest regular closed subalgebra coincides with the set of functions with natural spectra. Laursen and Neumann proved that if p=1 or G is compact, then RegC_0M_p (G) is the closed ideal C_<00>M_p (G) which consists of multplier whose Gelfand transforms vanish of the dual group of G.I proved that if p*1, then RegC_0M_p (R^n) is not an ideal of C_0M_p (R^n) and C_<00>M_p (R^n)= {0}. Let G be a non-discrete locally comapct abelian group. I prove that there exists a bounded regular Borel measure outside of the radical of L^1 (G) with a natural spectrum. In particular if G is not compact, then the Fourier-Stieltjes transform of the measure can be vanish at infinity on the dual group, which answers the question posed by Eschimier, Laursen and Neumann. I also study BSE-algebras.

在这项研究中，我研究了局部紧凑的阿贝尔组G的傅立叶乘数。确定了comact abelian群体上P-Q多置板的最大理想空间。特别是，我证明了G的双重组在最大的理想空间中是密集的，因此证明了P-Q乘数的Sspectra的自然性。还确定了P-2多板的操作功能。令C_0M_P（G）表示L^p-Multiplier的代数，其傅立叶变化在无穷大时会消失。我证明了Apostol代数与最大的常规闭合子代数REGC_0M_P（G）一致，从某种意义上说，它们在C_0M_P（G）中是最大的。证明取决于有关连续函数的抽象代数的一般结果，这些函数以傅立叶乘数为模型。我还证明，如果代数的最大理想空间在薄中，则它们是最大的常规闭合子代数与与天然光谱的一组函数相吻合。 Laursen and Neumann proved that if p=1 or G is compact, then RegC_0M_p (G) is the closed ideal C_<00>M_p (G) which consists of multplier whose Gelfand transforms vanish of the dual group of G.I proved that if p*1, then RegC_0M_p (R^n) is not an ideal of C_0M_p (R^n) and C_<00>M_p （r^n）= {0}。令G为非污染的本地comapct abelian群体。我证明，在L^1（g）的根部外，有一个有界的常规鲍尔尺寸，并具有自然光谱。特别是，如果G不紧凑，那么该度量的傅立叶变换可以在双重组上的无穷大范围内消失，这回答了Eschimier，Laursen和Neumann提出的问题。我还研究BSE-Elgebras。