A Dynamical Approach to the Perron-Frobenius Theory and Generalized Krein-Rutman Type Theorems
Li Desheng, Jia Mo
TL;DR
This paper introduces a dynamical method based on linear ODEs to extend the Perron-Frobenius theory and Krein-Rutman theorems, providing a new, self-contained approach that broadens their applicability.
Contribution
It develops a complex version of Perron-Frobenius theory and proves generalized Krein-Rutman theorems using an elementary dynamical approach.
Findings
A new dynamical framework for Perron-Frobenius theory
Extension to complex operators and spectra
Generalized Krein-Rutman theorems proven
Abstract
We present a dynamical approach to the classical Perron-Frobenius theory by using some elementary knowledge on linear ODEs. It is completely self-contained and significantly different from those in the literature. As a result, we develop a complex version of the Perron-Frobenius theory and prove some generalized Krein-Rutman type theorems.
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Taxonomy
TopicsTensor decomposition and applications · Algebraic structures and combinatorial models · Advanced Differential Equations and Dynamical Systems