In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Planch...In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.展开更多
The decomposition of the representations T0(v∈R) ore considered here. The Plancherel formula for the universal covering group of SU(1,1) is also deduced.
Let v∈C. We consider the complex measure dμ<sub>v</sub>（z） =（1-│z│<sup>2</sup>）<sup>v-2</sup>dxdy（z=x+iy） on theunit disk D of the complex plane. Let （D） be the spaces o...Let v∈C. We consider the complex measure dμ<sub>v</sub>（z） =（1-│z│<sup>2</sup>）<sup>v-2</sup>dxdy（z=x+iy） on theunit disk D of the complex plane. Let （D） be the spaces of C<sup>∞</sup>-function on D with compactsupports and #（B） the space of radial functions in （B）. The representation T<sup>v</sup> ofMbius group SU（1,1） on （D） is defined展开更多
Let / be a function on the unit ball of Rn. For , the action T of SO0 (1, n) on f isdefined by .The invariant Laplacian corresponding to T is calculated, and a family of its eigenfunctions is found out. Then the corre...Let / be a function on the unit ball of Rn. For , the action T of SO0 (1, n) on f isdefined by .The invariant Laplacian corresponding to T is calculated, and a family of its eigenfunctions is found out. Then the corresponding Fourier transform is defined and the inversion formula and Plancherel formula are obtained.展开更多
Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under t...Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.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
In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications o...In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.展开更多
基金supported by the National Natural Science Foundation of China(11201346)
文摘In this paper we obtain the Plancherel formula for the spaces of L2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G=SL（n ＋ 1, R） and H=S（GL（1, R）×GL（n, R））. The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.
文摘The decomposition of the representations T0(v∈R) ore considered here. The Plancherel formula for the universal covering group of SU(1,1) is also deduced.
文摘Let v∈C. We consider the complex measure dμ<sub>v</sub>（z） =（1-│z│<sup>2</sup>）<sup>v-2</sup>dxdy（z=x+iy） on theunit disk D of the complex plane. Let （D） be the spaces of C<sup>∞</sup>-function on D with compactsupports and #（B） the space of radial functions in （B）. The representation T<sup>v</sup> ofMbius group SU（1,1） on （D） is defined
文摘Let / be a function on the unit ball of Rn. For , the action T of SO0 (1, n) on f isdefined by .The invariant Laplacian corresponding to T is calculated, and a family of its eigenfunctions is found out. Then the corresponding Fourier transform is defined and the inversion formula and Plancherel formula are obtained.
基金Supported by the National Natural Science Foundation of China(No.10671176)
文摘Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.
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)
基金Supported by the National Natural Science Foundation of China(10931001, 10871173)
文摘In the paper, we establish the LP（Rn＋1）-boundedness for a class of singular integral operators associated to surfaces of revolution {（y,γ（｜y｜）, y ∈ Rn} with rough kernels. We also give several applications of this inequality.
