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- Ismail, Mourad E. H., et al.
(författare)
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Spectral analysis of two doubly infinite Jacobi matrices with exponential entries
- 2019
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 276:6, s. 1681-1716
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Tidskriftsartikel (refereegranskat)abstract
- We provide a complete spectral analysis of all self-adjoint operators acting on l(2)(Z) which are associated with two doubly infinite Jacobi matrices with entries given by q(-n+1) delta(m,n-1) + q(-n) delta(m,n+1) and delta(m,n-1) + alpha q(-n) delta(m,n) + delta(m,n+1), respectively, where q is an element of (0, 1) and alpha is an element of R. As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function.
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