## (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

154 |
Scattering Theory
- Lax, Phillips
- 1989
(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... |

20 |
On random Schrödinger operators on Z d
- Bourgain
- 2002
(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 ′... |

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

15 | W.: Classical and quantum scattering for a class of long range random potentials - Rodnianski, Schlag |

13 |
Asymptotic Methods
- Vainberg
- 1989
(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... |

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

6 | Surface states and spectra - Jaksic, Last |

6 | 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 | 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 |
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 ... |

3 | S.: Wave operators for the surface - Jaksic, Molchanov - 2000 |

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