## 20 Citations

Continuity of spectral radius over hyperbolic systems

- Mathematics
- 2018

The continuity of joint and generalized spectral radius is proved for Holder continuous cocycles over hyperbolic systems. We also prove the periodic approximation of Lyapunov exponents for…

On the spectral radius of compact operator cocycles

- Mathematics
- 2018

We extend the notions of joint and generalized spectral radii to cocycles acting on Banach spaces and obtain a version of Berger-Wang's formula when restricted to the space of cocycles taking values…

Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius

- MathematicsLinear Algebra and its Applications
- 2018

Ju n 20 13 Extremal norms for positive linear inclusions

- Mathematics
- 2013

For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is…

The joint spectrum

- MathematicsJournal of the London Mathematical Society
- 2020

We introduce the notion of joint spectrum of a compact set of matrices S⊂GLd(C) , which is a multi‐dimensional generalization of the joint spectral radius. We begin with a thorough study of its…

Mather sets for sequences of matrices and applications to the study of joint spectral radii

- Mathematics
- 2013

The joint spectral radius of a compact set of d×d matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. In this article, we investigate…

Continuity properties of the lower spectral radius

- Mathematics
- 2015

The lower spectral radius, or joint spectral subradius, of a set of real d×d matrices is defined to be the smallest possible exponential growth rate of long products of matrices drawn from that set.…

A note on the Joint Spectral Radius

- Mathematics
- 2015

Last two decades have been characterized by an increasing interest in theanalysis of the maximal growth rate of long products generated by matricesbelonging to a speci c set/family. The maximal…

## References

SHOWING 1-10 OF 25 REFERENCES

A relaxation scheme for computation of the joint spectral radius of matrix sets

- Mathematics
- 2011

The problem of computation of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In this paper, an iteration procedure is considered that allows to…

On explicit a priori estimates of the joint spectral radius by the generalized Gelfand formula

- Mathematics
- 2008

In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with…

Approximation of the joint spectral radius using sum of squares

- Mathematics, Computer Science
- 2008

On the structure of the set of extremal norms of a linear inclusion

- MathematicsProceedings of the 44th IEEE Conference on Decision and Control
- 2005

A systematic study of the set of extremal norms of an irreducible linear inclusion is undertaken. We recall basic methods for the construction of extremal norms, and consider the action of basic…

The characterization of continuous, four-coefficient scaling functions and wavelets

- MathematicsIEEE Trans. Inf. Theory
- 1992

Four-coefficient dilation equations are examined and results converse to a theorem of Daubechies-Lagarias are given. These results complete the characterization of those four-coefficient dilation…