## Details

Original language | English |
---|---|

Pages (from-to) | 217-232 |

Number of pages | 16 |

Journal | Integral Equations and Operator Theory |

Volume | 69 |

Issue number | 2 |

Publication status | Published - 1 Jan 2011 |

Externally published | Yes |

## Abstract

We study spectral properties of Schrödinger operators on. ℝ^{d}The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in ℤ^{d}, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e. the normalised eigenvalue counting functions. The convergence holds in the space L^{p}(I) where I is any finite energy interval and 1 ≤ p < ∞ is arbitrary.

## Keywords

- finite local complexity, Integrated density of states, random Schrödinger operators

## ASJC Scopus subject areas

- Mathematics(all)
**Analysis**- Mathematics(all)
**Algebra and Number Theory**

## Cite this

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**L**/ Gruber, Michael J.; Lenz, Daniel H.; Veselić, Ivan.

^{p}-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity.In: Integral Equations and Operator Theory, Vol. 69, No. 2, 01.01.2011, p. 217-232.

Research output: Contribution to journal › Article › Research › peer review

^{p}-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity',

*Integral Equations and Operator Theory*, vol. 69, no. 2, pp. 217-232. https://doi.org/10.1007/s00020-010-1831-6

^{p}-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity.

*Integral Equations and Operator Theory*,

*69*(2), 217-232. https://doi.org/10.1007/s00020-010-1831-6

^{p}-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity. Integral Equations and Operator Theory. 2011 Jan 1;69(2):217-232. doi: 10.1007/s00020-010-1831-6

}

TY - JOUR

T1 - Lp-Approximation of the Integrated Density of States for Schrödinger Operators with Finite Local Complexity

AU - Gruber, Michael J.

AU - Lenz, Daniel H.

AU - Veselić, Ivan

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We study spectral properties of Schrödinger operators on. ℝdThe electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in ℤd, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e. the normalised eigenvalue counting functions. The convergence holds in the space Lp(I) where I is any finite energy interval and 1 ≤ p < ∞ is arbitrary.

AB - We study spectral properties of Schrödinger operators on. ℝdThe electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in ℤd, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e. the normalised eigenvalue counting functions. The convergence holds in the space Lp(I) where I is any finite energy interval and 1 ≤ p < ∞ is arbitrary.

KW - finite local complexity

KW - Integrated density of states

KW - random Schrödinger operators

UR - http://www.scopus.com/inward/record.url?scp=78751648251&partnerID=8YFLogxK

U2 - 10.1007/s00020-010-1831-6

DO - 10.1007/s00020-010-1831-6

M3 - Article

AN - SCOPUS:78751648251

VL - 69

SP - 217

EP - 232

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 2

ER -