International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 29-32, Pages 1703-1714
doi:10.1155/S0161171204007392
On the expansion theorem described by H(A,B) spaces
A.A. El-Sabbagh
Department of Mathematics, Faculty of Engineering, Zagazig University, 108 Shoubra Street, Shoubra, Cairo, Egypt
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.