Abstract
We derive an explicit expression for the kernel of the evolution group \({\exp(-\mathrm{i} t H_0)}\) of the discrete Laguerre operator H 0 (i.e., the Jacobi operator associated with the Laguerre polynomials) in terms of Jacobi polynomials. Based on this expression, we show that the norm of the evolution group acting from \({\ell^1}\) to \({\ell^\infty}\) is given by \({(1+t^2)^{-1/2}}\).
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Research supported by the Austrian Science Fund (FWF) under Grant No. P26060. Open access funding provided by University of Vienna.
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Kostenko, A., Teschl, G. Dispersion Estimates for the Discrete Laguerre Operator. Lett Math Phys 106, 545–555 (2016). https://doi.org/10.1007/s11005-016-0831-0
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DOI: https://doi.org/10.1007/s11005-016-0831-0