A Hypergeometric Function Transform and Matrix-Valued Orthogonal Polynomials

作者：Groenevelt Wolter^*; Koelink Erik

来源：Constructive Approximation, 2013, 38(2): 277-309.

DOI：10.1007/s00365-013-9207-1

• Hypergeometric function transform
• Matrix-valued orthogonal polynomials
• Second-order differential operator
• Five-term operator
• Spectral analysis

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, leading to orthogonality relations for 2x2-matrix-valued polynomials. These matrix-valued polynomials can be considered as matrix-valued generalizations of Wilson polynomials.

• 出版日期2013-10