The Strong Perron Integral

THE STRONG PERRON INTEGRAL IN THE n-DIMENSIONAL SPACE R

In this paper, we introduce the SP -integral and the SPα-integral defined on an interval in the n-dimensional Euclidean space Rn. We also investigate the relationship between these two integrals.

Achievable spectral radii of symplectic Perron–Frobenius matrices

A pseudo-Anosov surface automorphism φ has associated to it an algebraic unit λφ called the dilatation of φ. It is known that in many cases λφ appears as the spectral radius of a Perron–Frobenius matrix preserving a symplectic form L. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit λ appears as an eigenvalue for some integra...

O ct 2 00 6 Cones and gauges in complex spaces : Spectral gaps and complex Perron - Frobenius theory

We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone-contraction Theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch’s Theorem to complex integral operator...

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Ela Paths of Matrices with the Strong Perron-frobenius Property Converging to a given Matrix with the Perron-frobenius Property∗

A matrix is said to have the Perron-Frobenius property (strong Perron-Frobenius property) if its spectral radius is an eigenvalue (a simple positive and strictly dominant eigenvalue) with a corresponding semipositive (positive) eigenvector. It is known that a matrix A with the Perron-Frobenius property can always be the limit of a sequence of matrices A(ε) with the strong Perron-Frobenius prope...