Abstract

The aim of this paper is to construct a generalized Fourier analysis for certain Hermitian operators. When A, B are entire functions, then H(A,B) will be the associated reproducing kernel Hilbert spaces of ℂn×n-valued functions. In that case, we will construct the expansion theorem for H(A,B) in a comprehensive manner. The spectral functions for the reproducing kernel Hilbert spaces will also be constructed.