Dispersion Estimates for the Discrete Laguerre Operator

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• 作者：Aleksey Kostenko ; Gerald Teschl
• 关键词：Schrödinger equation ; dispersive estimates ; Laguerre polynomials
• 刊名：Letters in Mathematical Physics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：106
• 期：4
• 页码：545-555
• 全文大小：435 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Statistical Physics
  Geometry
  Group Theory and Generalizations
  
• 出版者：Springer Netherlands
• ISSN：1573-0530

文摘

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