We investigate in a geometrical way the sieving process of 021 β 3 for obtaining the Delone set 0 β 4 051 β 3 of β integers where β is a Perron number in the context of linear asymptotic invariants associated with a canonical inductive system constructed from β . When β is a Pisot number, we exhibit a canonical cut-and-project scheme, a model set associated with 0 β and so prove that it is a Me...

The analysis of the Perron eigenspace of a nonnegative matrix A whose symmetric part has rank one is continued. Improved bounds for the Perron root of Levinger’s transformation (1 − α)A+ αAt (α ∈ [0, 1]) and its derivative are obtained. The relative geometry of the corresponding left and right Perron vectors is examined. The results are applied to tournament matrices to obtain a comparison resu...

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Let A be a nonnegative square matrix whose symmetric part has rank one. Tournament matrices are of this type up to a positive shift by 1/2I . When the symmetric part of A is irreducible, the Perron value and the left and right Perron vectors of L(A, α) = (1 − α)A+ αAt are studied and compared as functions of α ∈ [0, 1/2]. In particular, upper bounds are obtained for both the Perron value and it...

A Perron number is a real algebraic integer α of degree d ≥ 2, whose conjugates are αi, such that α > max2≤i≤d |αi|. In this paper we compute the smallest Perron numbers of degree d ≤ 24 and verify that they all satisfy the Lind-Boyd conjecture. Moreover, the smallest Perron numbers of degree 17 and 23 give the smallest house for these degrees. The computations use a family of explicit auxiliar...

In this paper, we study the strong Perron integral, and show that the strong Perron integral is equivalent to the McShane integral.

We consider the Fröbenius–Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ–finite regular measure. Assuming strong continuity for the Fröbenius–Perron semigroup of linear operators in the space Lμ(X) or in the space Lμ(X) for 1 < p <∞ ([11]). We study in this article ergodic properties of the Fröbenius–Perron...

The concept of the Perron complement of a nonnegative and irreducible matrix was introduced by Meyer in 1989 and it was used to construct an algorithm for computing the stationary distribution vector for Markov chains. Here properties of the generalized Perron complement of an n×n irreducible Z-matrixK are considered. First the result that the generalized Perron complements of K are irreducible...