We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β...We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.展开更多
We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the g...We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.展开更多
文摘We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.
文摘We discuss the initial boundary value problem of a class of nonlinear Schr6dinger equations with potential functions. By the theory of the group of unitary operators and the method ofthe prior estimate, we prove the global existence of the classical solutions of the nonlinear Schrodingerequations with potential functions.
