标题： 紧致对称空间上塞格尔-巴格曼变换的等距定理 显示英文标题

标题： Isometry theorem for the Segal-Bargmann transform on noncompact symmetric spaces of the complex type

摘要： 我们考虑复类型非紧对称空间的Segal-Bargmann变换。 我们在尽可能与紧情况结果平行的形式下，建立了该变换的等距性和满射性定理。 等距性定理涉及在复化空间中半径为R的管域上的积分，随后进行关于R的解析延拓。奇异性的抵消使得相关积分即使在被积函数存在奇异性的前提下，也能扩展到大的R值而没有奇异性的出现。 显示英文摘要

摘要： We consider the Segal-Bargmann transform for a noncompact symmetric space of the complex type. We establish isometry and surjectivity theorems for the transform, in a form as parallel as possible to the results in the compact case. The isometry theorem involves integration over a tube of radius R in the complexification, followed by analytic continuation with respect to R. A cancellation of singularities allows the relevant integral to have a nonsingular extension to large R, even though the function being integrated has singularities.