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 ℝ with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform ℱ with two different big q-Jacobi functions as a kernel, and we construct the inverse of ℱ.
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Communicated by Mourad Ismail.
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Groenevelt, W. The Vector-Valued Big q-Jacobi Transform. Constr Approx 29, 85–127 (2009). https://doi.org/10.1007/s00365-008-9009-z
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DOI: https://doi.org/10.1007/s00365-008-9009-z
Keywords
- Vector-valued big q-Jacobi transform
- Difference operator
- Spectral analysis
- Big q-Jacobi polynomials
- Integral transform