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The vector-valued big q-Jacobi transform

Wolter Groenevelt
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Abstract

Big $q$-Jacobi functions are eigenfunctions of a second order $q$-difference operator $L$. We study $L$ as an unbounded self-adjoint operator on an $L^2$-space of functions on $\mathbb R$ with a discrete measure. We describe explicitly the spectral decomposition of $L$ using an integral transform $\mathcal F$ with two different big $q$-Jacobi functions as a kernel, and we construct the inverse of $\mathcal F$.

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Wolter Groenevelt. 2007-01-11. The vector-valued big q-Jacobi transform. https://arxiv.org/abs/math/0612643

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