The vector-valued big q-Jacobi transform

Details The vector-valued big q-Jacobi transform The vector-valued big q-Jacobi transform

2006-12-21

arxiv.org/abs/math/0612643v2

Constr. Approx. 29 (2009), no. 1, 85-127

Mathematics

Classical Analysis and ODEs

35 pages, corrected an error and typos

Scientific paper

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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