With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed int...With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ 1+μ 2, whereμ 1 is a bounded measure on 0<=s<=2 andμ 2 is slowly increasing measure on (sχC|Re(s)=1)}展开更多
Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, an...Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.展开更多
基金the National Natural Science F oundation of China (198710 65 ) and Hua Cheng Mathematics Science Foundation
文摘With the aid of Plancherel-Godement Theorem, we prove that every positive distributionT onSO (3, 1) which is bi-invariant underSO(3) corresponds to a measure μ on ω=∝σC|s(2-s)>=0∝, and μ can be decomposed intoμ=μ 1+μ 2, whereμ 1 is a bounded measure on 0<=s<=2 andμ 2 is slowly increasing measure on (sχC|Re(s)=1)}
文摘Using the method of Clerc and Stein study the multipliers of spherical Fourier transform on symmetric space to proof the multipliers theory for the space SL(3,H)/SP(3), completely avoid the complex theory of Anker, and we have gain the same result. Key words Riemannian symmetric space SL(3,H)/SP(3) - multipliers - spherical Fourier transform - invariant differential operator CLC number O 152.5 - O 186.12 Biography: LIAN Bao-sheng (1973-), male, Master, research direction: Li group and Lie algebra.
