## (2005)

### BibTeX

@MISC{Islami05,

author = {H. Islami and B. Vainberg},

title = {},

year = {2005}

}

### OpenURL

### Abstract

Large time behavior of the solutions to the difference wave operators.

### Citations

195 |
Scattering theory
- Lax, Phillips
- 1967
(Show Context)
Citation Context ...he function f is also real valued. ∗ Corresponding author, email: brvainbe@uncc.edu. The work by B. Vainberg was supported partially by the NSF grant DMS-0405927. 1This question is well studied (see =-=[8]-=-,[14]) in the continuous case, i.e., for operators H on L 2 (R n ) . In this case the answer depends on analytical properties of the truncated resolvent ˆRλ = χ (H − λ) −1 χ where χ ∈ C ∞ 0 . In the 2... |

21 |
A remark on Schrodinger operators
- BOURGAIN
- 1992
(Show Context)
Citation Context ...cs, lattice, Cauchy problem. I. Introduction. In the recent years there has been considerable interest in the scattering theory of discrete Schrödinger operator on the lattice Z d ( see, for example, =-=[1]-=--[7],[9]-[13]). The two dimensional Schrödinger operator on the lattice Z 2 Hu = −∆u + q (ξ)u, ξ ∈ Z 2 is considered in this paper. Here ∆ is the lattice Laplacian ∆u (ξ) = ∑ u (ξ ′ ) − 4u (ξ). |ξ−ξ ′... |

20 |
Asymptotic Methods
- Vainberg
- 1988
(Show Context)
Citation Context ...unction f is also real valued. ∗ Corresponding author, email: brvainbe@uncc.edu. The work by B. Vainberg was supported partially by the NSF grant DMS-0405927. 1This question is well studied (see [8],=-=[14]-=-) in the continuous case, i.e., for operators H on L 2 (R n ) . In this case the answer depends on analytical properties of the truncated resolvent ˆRλ = χ (H − λ) −1 χ where χ ∈ C ∞ 0 . In the 2-D co... |

17 | Classical and quantum scattering for a class of long range random potentials - Rodnianski, Schlag |

15 | On the spectral and scattering theory of the Schrödinger operator with surface potential - Chahrour, Sahbani - 2000 |

8 | Spectral theory of sparse potentials - Hundertmark, Kirsch - 1999 |

7 | On the propagation properties of surface waves
- Jaksic, Molchanov, et al.
- 1998
(Show Context)
Citation Context ...lattice, Cauchy problem. I. Introduction. In the recent years there has been considerable interest in the scattering theory of discrete Schrödinger operator on the lattice Z d ( see, for example, [1]-=-=[7]-=-,[9]-[13]). The two dimensional Schrödinger operator on the lattice Z 2 Hu = −∆u + q (ξ)u, ξ ∈ Z 2 is considered in this paper. Here ∆ is the lattice Laplacian ∆u (ξ) = ∑ u (ξ ′ ) − 4u (ξ). |ξ−ξ ′ |=1... |

6 | Surface states and spectra - Jaksic, Last |

6 | Scattering on the system of sparse bumps: multidimensional case - Molchanov, Vainberg - 1999 |

5 | On the spectral and wave propagation properties of the surface - Briet |

4 | Wave operators for the surface - Jakšić, Molchanov - 2000 |

4 |
Radiation conditions for the difference Schrödinger operators, Applicable Anal
- Shaban, Vainberg
(Show Context)
Citation Context ... Cauchy problem. I. Introduction. In the recent years there has been considerable interest in the scattering theory of discrete Schrödinger operator on the lattice Z d ( see, for example, [1]-[7],[9]-=-=[13]-=-). The two dimensional Schrödinger operator on the lattice Z 2 Hu = −∆u + q (ξ)u, ξ ∈ Z 2 is considered in this paper. Here ∆ is the lattice Laplacian ∆u (ξ) = ∑ u (ξ ′ ) − 4u (ξ). |ξ−ξ ′ |=1 and the ... |

1 | Molchanov-Vainberg Laplacian, preprint - Poulin - 2004 |