Research on Fourier multiplier by operating functions on function spaces
Project/Area Number  06804010 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Niigata University 
Principal Investigator 
HATORI Osamu Niigata University Griduate School of Science and Technology Associate Professor, 自然科学研究科, 助教授 (70156363)

Project Fiscal Year 
1994 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1996 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1995 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1994 : ¥400,000 (Direct Cost : ¥400,000)

Keywords  commutative Banach algebra / multiplier / operating function / function space / locally compact abelian group / WienerPitt phenomenum / 可換Banach環 / 作用関数 / 関数空間 / 局所コンパクトアーベル群 / WienerPitt現象 / L^Pmultiplier / 極大イデアル空間 / locallycompact abelian group / regular Banach algebra / decomposable operator / natural spectrum 
Research Abstract 
In this research I study Fourier multiplier on locally compact abelian groups G.The maximal ideal space of pq 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 pq multiplier is proved. The operating functions of p2 multplier is also identified. Let C_0M_p (G) denote the algebra of L^pmultiplier 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 nondiscrete 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 FourierStieltjes 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 BSEalgebras.

Report
(5results)
Research Output
(23results)