Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates

Abstract

We consider the Schrödinger equation with a Hamiltonian given by a second order difference operator with nonconstant growing coefficients, on the half one dimensional lattice. This operator appeared first naturally in the construction and dynamics of noncommutative solitons in the context of noncommutative field theory. We prove pointwise in time decay estimates, with the optimal decay rate $t^{-1}{\log }^{-2}t$ generically. We use a novel technique involving generating functions of orthogonal polynomials to achieve this estimate.

25 pages

References in corpus (4)

• Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity
• Noncommutative Solitons
• Structure of Noncommutative Solitons: Existence and Spectral Theory
• Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates

Cited by in corpus (5)

• Jacobi Polynomials, Bernstein-type Inequalities and Dispersion Estimates for the Discrete Laguerre Operator
• Dynamics of Noncommutative Solitons I: Spectral Theory and Dispersive Estimates
• Heat kernels of the discrete Laguerre operators
• Dispersion Estimates for the Discrete Laguerre Operator
• Trace formulas and inverse spectral theory for generalized indefinite strings