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 H0) of the discrete Laguerre operator H0 (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 l1 to l is given by (1+t2)-1/2.

MSC2010: Primary 35Q41, 47B36; Secondary 81U30, 81Q05
Keywords: Schrödinger equation, dispersive estimates, Laguerre polynomials

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