Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions
Abstract
The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schr\"odinger type and an integral operator of Fourier type. As a consequence we derive integral representations of these functions as well as other useful structural formulas. Some of these functions are plotted to show the relationship with the Hermite or wave functions.
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