Properties of the scattering matrix and dispersion estimates for Jacobi operators
Copyright policy )Properties of the scattering matrix and dispersion estimates for Jacobi operators
We show that for a Jacobi operator with coefficients whose (j+1)'th moments are summable the j'th derivative of the scattering matrix is in the Wiener algebra of functions with summable Fourier coefficients. We use this result to improve the known dispersive estimates with integrable time decay for the time dependent Jacobi equation in the resonant case.
10 pages
- University of Vienna Austria
- Schrödinger United States
WAVES, Jacobi (tridiagonal) operators (matrices) and generalizations, FOS: Physical sciences, 101002 Analysis, LONG-TIME ASYMPTOTICS, Scattering, Mathematics - Spectral Theory, resonant case, Resonant case, Dispersion theory, dispersion relations arising in quantum theory, EQUATION, FOS: Mathematics, dispersive estimates, Spectral Theory (math.SP), Mathematical Physics, STABILITY, scattering, Primary 35Q41, 34L25, Secondary 81U30, 47B36, Mathematical Physics (math-ph), Jacobi operator, TODA LATTICE, Time-dependent Schrödinger equations and Dirac equations, DISCRETE NONLINEAR SCHRODINGER, Dispersive estimates
WAVES, Jacobi (tridiagonal) operators (matrices) and generalizations, FOS: Physical sciences, 101002 Analysis, LONG-TIME ASYMPTOTICS, Scattering, Mathematics - Spectral Theory, resonant case, Resonant case, Dispersion theory, dispersion relations arising in quantum theory, EQUATION, FOS: Mathematics, dispersive estimates, Spectral Theory (math.SP), Mathematical Physics, STABILITY, scattering, Primary 35Q41, 34L25, Secondary 81U30, 47B36, Mathematical Physics (math-ph), Jacobi operator, TODA LATTICE, Time-dependent Schrödinger equations and Dirac equations, DISCRETE NONLINEAR SCHRODINGER, Dispersive estimates
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