International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 32, Pages 1703-1714

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

Received 28 February 2000

Copyright © 2004 A. A. El-Sabbagh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 n×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.