Laguerre polynomials and Perron-Frobenius operators

Weighted Frobenius-Perron and Koopman operators

Spectrum Properties of the Koopman and Frobenius-Perron Operators

Compact weighted Frobenius-Perron operators and their spectra

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.

A primer of Perron–Frobenius theory for matrix polynomials

We present an extension of Perron–Frobenius theory to the spectra and numerical ranges of Perron polynomials, namely, matrix polynomials of the form L(λ) = Iλ − Am−1λm−1 − · · · − A1λ− A0, where the coefficient matrices are entrywise nonnegative. Our approach relies on the companion matrix linearization. First, we recount the generalization of the Perron–Frobenius Theorem to Perron polynomials ...

PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.