A Hypergeometric Function Transform and Matrix-valued Orthogonal Polynomials
نویسنده
چکیده
The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomials the operator T can also be realized as a five-diagonal operator, hence leading to orthogonality relations for 2 × 2-matrix-valued polynomials. These matrix-valued polynomials can be considered as matrix-valued generalizations of Wilson polynomials.
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