非紧致一秩对称空间Cartan运动群上的Radon变换

非紧致一秩对称空间Cartan运动群上的Radon变换 THE RADON TRANSFORMATION ON CART AN MOTION GROUP ASSOCIATED TO A NONCOMPACT SYMMETRIC SPACE OF RANK ONE 朱赋鎏 Zhu Fuliu 1 first-author 武汉大学数学系,武汉,430072 武汉大学数学系,武汉,430072 Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 本文研究与非紧致一秩Riemann对称空间相应的Cartan运动群上的Radon变换,用Weyl分式积分求出了这种变换的逆,并用这种逆Radon变换导出Fourier代数中元素的局部正则性,最后证明了任一正则K-轨道不是Fourier代数的谱综合集。 This paper studies the Radon transformation of Cartan motion group associ-ated to a noncompact Riemannian symmetric space of rank one. We obtain the inverse of this transformation by using Weyl’s fractional integral,and induce the locale regularity of an ele-ment of the Fourier algebra. Finally,we prove that every regular K-orbit isn’t a set synthese spectrale of the Fourier algebra. 一秩对称空间 Cartan运动群 Radon变换 Fourier代数 谱综合集 symmetric space of rank one cartan motion group radon transformation fourier algebra set of spectral synthese O;O186.1 国家自然科学基金资助的课题 1994-05-01 2021-04-01 5