The Vector-Valued Big <Emphasis Type="Italic">q</Emphasis>-Jacobi Transform |
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| Authors: | Wolter Groenevelt |
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| Institution: | (1) Technische Universiteit Delft, EWI-DIAM, Postbus 5031, 2600 GA Delft, The Netherlands |
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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 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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| Keywords: | Vector-valued big q-Jacobi transform Difference operator Spectral analysis Big q-Jacobi polynomials Integral transform |
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