scholarly journals The essential spectral radius of dominated positive operators

1993 ◽  
Vol 118 (2) ◽  
pp. 419-419
Author(s):  
Josep Mart{í}nez
Keyword(s):  
Spectral Radius ◽  
Positive Operators ◽  
Essential Spectral Radius

scholarly journals Decay of correlations in suspension semi-flows of angle-multiplying maps

2008 ◽  
Vol 28 (1) ◽  
pp. 291-317 ◽  
Author(s):  
MASATO TSUJII
Keyword(s):  
Hilbert Space ◽  
Sobolev Space ◽  
Spectral Radius ◽  
Decay Of Correlations ◽  
Square Root ◽  
Precise Description ◽  
Anisotropic Sobolev Space ◽  
Essential Spectral Radius ◽  
Frobenius Operator ◽  
Dense Set

AbstractWe consider suspension semi-flows of angle-multiplying maps on the circle for Cr ceiling functions with r≥3. Under a Crgeneric condition on the ceiling function, we show that there exists a Hilbert space (anisotropic Sobolev space) contained in the L2 space such that the Perron–Frobenius operator for the time-t-map acts naturally on it and that the essential spectral radius of that action is bounded by the square root of the inverse of the minimum expansion rate. This leads to a precise description of decay of correlations. Furthermore, the Perron–Frobenius operator for the time-t-map is quasi-compact for a Cr open and dense set of ceiling functions.

Bounds for the spectral radius of positive operators

1967 ◽  
Vol 1 (4) ◽  
pp. 306-310 ◽  
Author(s):  
P. P. Zabreiko ◽  
M. A. Krasnosel'skii ◽  
V. Ya. Stetsenko
Keyword(s):  
Spectral Radius ◽  
Positive Operators

Spectral properties of a class of operators associated with maps in one dimension

1991 ◽  
Vol 11 (4) ◽  
pp. 757-767 ◽  
Author(s):  
David Ruelle
Keyword(s):  
Spectral Radius ◽  
Bounded Variation ◽  
One Dimension ◽  
Functions Of Bounded Variation ◽  
Finite Multiplicity ◽  
Piecewise Monotone ◽  
Essential Spectral Radius ◽  
Monotone Map ◽  
Image Position ◽  
Isolated Eigenvalues

AbstractLet f be a piecewise monotone map of the interval [0,1] to itself, and g a function of bounded variation on [0, 1]. Hofbauer, Keller and Rychlik have studied operators on functions of bounded variation, whereAmong other things, they show that the essential spectral radius of is in many cases strictly smaller than the spectral radius; there exist therefore isolated eigenvalues of finite multiplicity. The purpose of the present paper is to prove similar results for a more general class of operators forming an algebra (and therefore containing sums of operators like ). An analogous extension was presented by Ruelle for operators associated with expanding maps.

Reliability Analysis of a Two-Unit System with Connecting and Disconnecting Effect

2012 ◽  
Vol 263-266 ◽  
pp. 723-730
Author(s):  
Pei Rang Peng ◽  
Chun Li ◽  
Wei Hua Guo
Keyword(s):  
Functional Analysis ◽  
Exponential Stability ◽  
Reliability Analysis ◽  
Spectral Radius ◽  
Semi Group ◽  
Unit System ◽  
Essential Spectral Radius ◽  
Before And After ◽  
System Operator ◽  
Growth Bound

A Two-Unit system with connecting and disconnecting effect is studied in this paper. By the method of Functional analysis strong continuous semi-group, the paper analyzes the restriction of essential spectral growth bound of the system operator. The restriction of essential spectral growth bound of the system operator and the change of the essential spectral radius after perturbation is analyzed. The essential spectral radius of the system operator is also discussed before and after perturbation. The results show that under some conditions the dynamic solution of the system is exponential stability and tends to the steady solution of the system. At last, we analyze the reliability of the system.

scholarly journals Computable bounds of an 𝓁²-spectral gap for discrete Markov chains with band transition matrices

2016 ◽  
Vol 53 (3) ◽  
pp. 946-952
Author(s):  
Loï Hervé ◽  
James Ledoux
Keyword(s):  
Convergence Rate ◽  
Markov Chains ◽  
Spectral Radius ◽  
Spectral Gap ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Geometric Ergodicity ◽  
Transition Matrices ◽  
Essential Spectral Radius ◽  
Band Transition

AbstractWe analyse the 𝓁²(𝜋)-convergence rate of irreducible and aperiodic Markov chains with N-band transition probability matrix P and with invariant distribution 𝜋. This analysis is heavily based on two steps. First, the study of the essential spectral radius ress(P|𝓁²(𝜋)) of P|𝓁²(𝜋) derived from Hennion’s quasi-compactness criteria. Second, the connection between the spectral gap property (SG2) of P on 𝓁²(𝜋) and the V-geometric ergodicity of P. Specifically, the (SG2) is shown to hold under the condition α0≔∑m=−NNlim supi→+∞(P(i,i+m)P*(i+m,i)1∕2<1. Moreover, ress(P|𝓁²(𝜋)≤α0. Effective bounds on the convergence rate can be provided from a truncation procedure.

scholarly journals Linear maps preserving the essential spectral radius

2008 ◽  
Vol 428 (4) ◽  
pp. 1041-1045 ◽  
Author(s):  
M. Bendaoud ◽  
A. Bourhim ◽  
M. Sarih
Keyword(s):  
Spectral Radius ◽  
Essential Spectral Radius ◽  
Linear Maps
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