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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

international journal of mathematics and mathematical sciences

On the expansion theorem described by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$H(A,B)$"><mml:mi>H</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>spaces

On the expansion theorem described byH(A,B)spaces