scholarly journals Substitution Delone sets with pure point spectrum are inter-model sets

2007 ◽  
Vol 57 (11) ◽  
pp. 2263-2285 ◽  
Author(s):  
Jeong-Yup Lee
Keyword(s):  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Model Sets ◽  
Delone Sets

scholarly journals Pure Point Spectrum of the Laplacians on Fractal Graphs

1995 ◽  
Vol 129 (2) ◽  
pp. 390-405 ◽  
Author(s):  
L. Malozemov ◽  
A. Teplyaev
Keyword(s):  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum

scholarly journals Global multiplicity bounds and spectral statistics for random operators

2020 ◽  
Vol 32 (09) ◽  
pp. 2050025
Author(s):  
Anish Mallick ◽  
Krishna Maddaly
Keyword(s):  
Lower Bound ◽  
Separable Hilbert Space ◽  
Point Spectrum ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Positive Lebesgue Measure ◽  
Spectral Multiplicity ◽  
Local Statistics ◽  
Higher Rank ◽  
Spectral Statistics

In this paper, we consider Anderson type operators on a separable Hilbert space where the random perturbations are finite rank and the random variables have full support on [Formula: see text]. We show that spectral multiplicity has a uniform lower bound whenever the lower bound is given on a set of positive Lebesgue measure on the point spectrum away from the continuous one. We also show a deep connection between the multiplicity of pure point spectrum and local spectral statistics, in particular, we show that spectral multiplicity higher than one always gives non-Poisson local statistics in the framework of Minami theory. In particular, for higher rank Anderson models with pure point spectrum, with the randomness having support equal to [Formula: see text], there is a uniform lower bound on spectral multiplicity and in case this is larger than one, the local statistics is not Poisson.

scholarly journals Pseudo-autonomous linear systems

1977 ◽  
Vol 16 (1) ◽  
pp. 61-65 ◽  
Author(s):  
W.A. Coppel
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Systems ◽  
Point Spectrum ◽  
Coefficient Matrix ◽  
Linear Differential Equations ◽  
Pure Point ◽  
Pure Point Spectrum ◽  
Linear Differential

Pseudo-autonomous linear differential equations are defined. A linear differential equation with bounded coefficient matrix is pseudo-autonomous if and only if it is almost reducible. A linear differential equation with recurrent coefficient matrix is pseudo-autonomous if and only if it has pure point spectrum.

Sign in / Sign up

Export Citation Format

Share Document