Square Integrable and Holomorphic Kernels

Abstract

This chapter is devoted to a systematic study of two special types of reproducing kernel Hilbert spaces, namely, those corresponding to square integrable kernels and to holomorphic kernels. The first case is illustrated by the construction of CS on the circle. This example suggests introducing action-angle variables, which are then used to extend the theory to a non-holomorphic set-up, namely, the so-called Gazeau–Klauder CS. The latter in turn lead to probabilistic considerations, that will be the focus of Chap. 11.KeywordsHilbert SpaceHolomorphic FunctionCoherent StateIntegrable KernelReproduce Kernel Hilbert SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.