Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions - Mathematics > Functional AnalysisReport as inadecuate




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Abstract: The aim of this paper is to show some examples of matrix-valued orthogonalfunctions on the real line which are simultaneously eigenfunctions of asecond-order differential operator of Schr\-{o}dinger type and an integraloperator of Fourier type. As a consequence we derive integral representationsof these functions as well as other useful structural formulas. Some of thesefunctions are plotted to show the relationship with the Hermite or wavefunctions.



Author: Manuel D. de la Iglesia

Source: https://arxiv.org/







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