Analytic reproducing kernels and multiplication operators (Q1203508)

A correspondence is established between the range spaces of the bounded linear operators on the sequence space \(\ell_ +^ 2\) and a large class of reproducing kernel Hilbert spaces. Via this correspondence, the multiplication operators on the functional Hilbert spaces are modeled as Toeplitz operators on the range spaces. A general investigation is begun in which properties of the multiplication operators are related to properties of the range spaces. An algorithmic method for constructing an orthonormal basis in a reproducing kernel Hilbert space is presented.