Spectral analysis of two doubly infinite Jacobi matrices with exponential entries
Autor: | František Štampach, Mourad E. H. Ismail |
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Rok vydání: | 2019 |
Předmět: | |
Zdroj: | Journal of Functional Analysis. 276:1681-1716 |
ISSN: | 0022-1236 |
Popis: | 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 δ m , n − 1 + q − n δ m , n + 1 and δ m , n − 1 + α q − n δ m , n + δ m , n + 1 , respectively, where q ∈ ( 0 , 1 ) and α ∈ R . As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function. |
Databáze: | OpenAIRE |
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