ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46,42,32 Morimoto, Mitsuo, International Christian University, and Keiko Fujita, Saga University Reproducing kernels related to the complex sphere We shall introduce four Hilbert spaces with a reproducing kernel and study relations among them. These Hilbert spaces are related to Fourier transforms of analytic functionals on the complex sphere

S̃_{λ} = {(z_{1}, z_{2}, ⋯, z_{n+1}) ∈ C^{n+1}; z_{1}^{2} + z_{2}^{2} + ⋯ + z_{n+1}^{2} = λ^{2}},

λ being a complex number. One of the four Hilbert spaces is the Hardy space on the truncated complex sphere S_{λ} ∩ B̃(r), where B̃(r) is the Lie ball of radius r > |λ|. General background of the talk is described in the forthcoming book “Analytic Functionals on the Sphere” by M. Morimoto (Monograph of AMS).