In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obta...In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application.展开更多
利用Lie群分析和古典分析的方法得到了SL(2,R)上的可微函数的Fourier变换的渐近阶:若f(x)∈Cck(SL(2,R)),R≥1,则 ||f(j,1/2+iλ)||HS=0(λ-k),j=0,1/2,λ→∞, ||f(n)||HS=0(|n|-k),n→∞.作为上面结果的一个应用,得到了Cc2(SL(2,R))上...利用Lie群分析和古典分析的方法得到了SL(2,R)上的可微函数的Fourier变换的渐近阶:若f(x)∈Cck(SL(2,R)),R≥1,则 ||f(j,1/2+iλ)||HS=0(λ-k),j=0,1/2,λ→∞, ||f(n)||HS=0(|n|-k),n→∞.作为上面结果的一个应用,得到了Cc2(SL(2,R))上的Plancherel定理. --原文发表于《Analysis in Theorg and Applications》,2003,19(1)展开更多
文摘In this paper, a better asymptotic order of Fourier transform on SL(2,R) is obtained by using classical analysis and Lie analysis comparing with that of [5],[6] ,and the Plancherel theorem on C2i(SL(2,R)) is also obtained as an application.
文摘利用Lie群分析和古典分析的方法得到了SL(2,R)上的可微函数的Fourier变换的渐近阶:若f(x)∈Cck(SL(2,R)),R≥1,则 ||f(j,1/2+iλ)||HS=0(λ-k),j=0,1/2,λ→∞, ||f(n)||HS=0(|n|-k),n→∞.作为上面结果的一个应用,得到了Cc2(SL(2,R))上的Plancherel定理. --原文发表于《Analysis in Theorg and Applications》,2003,19(1)
