Spectral analysis of two doubly infinite Jacobi matrices with exponential entries |
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Authors: | Mourad EH Ismail Franti?ek ?tampach |
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Institution: | 1. Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA;2. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia;3. Department of Mathematics, Stockholm University, Kräftriket 5, SE-106 91 Stockholm, Sweden;4. Department of Applied Mathematics, Faculty of Information Technology, Czech Technical University in Prague, Thákurova 9, 160 00 Prague, Czech Republic |
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Abstract: | We provide a complete spectral analysis of all self-adjoint operators acting on which are associated with two doubly infinite Jacobi matrices with entries given by and respectively, where and . As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function. |
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Keywords: | 47B36 33D90 Doubly infinite Jacobi matrix Discrete Schrödinger operator Theta function Corresponding author |
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