Article

**Lett. Math. Phys. 106, 545-555 (2016)**[DOI: 10.1007/s11005-016-0831-0]

## Dispersion Estimates for the Discrete Laguerre Operator

### Aleksey Kostenko and Gerald Teschl

We derive an explicit expression for the kernel of the evolution group

*exp(-i t H*of the discrete Laguerre operator_{0})*H*(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_{0}*l*to^{1}*l*is given by^{∞}*(1+t*.^{2})^{-1/2}
** MSC2010:** Primary 35Q41, 47B36; Secondary 81U30, 81Q05

**Keywords:** *Schrödinger equation, dispersive estimates, Laguerre polynomials*

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