Dispersion Estimates for the Discrete Laguerre Operator

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 $(1+t^2{)}^{-1/2}$.

9 pages

References in corpus (6)

• Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations
• Dispersion Estimates for One-Dimensional Discrete Dirac Equations
• Noncommutative Solitons
• Structure of Noncommutative Solitons: Existence and Spectral Theory
• Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates
• Properties of the Scattering Matrix and Dispersion Estimates for Jacobi Operators

Cited by in corpus (2)

• Jacobi Polynomials, Bernstein-type Inequalities and Dispersion Estimates for the Discrete Laguerre Operator
• Heat kernels of the discrete Laguerre operators