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In this paper, we survey valuable results to analyze discrete models frequently appearing in social and natural sciences. We review some well-known results and tools to analyze these systems, trying to make them as practical as possible so that not only mathematicians but also physicists, economists or biologists can use them to explore their models. Applying these methods requires some basic knowledge of computational tools and basic programming. The reviewed topics vary from the local stability of equilibrium points to the characterization of topological and physically observable chaos.
In this paper, having analyzed the previously obtained results devoted to the root vectors series expansion in the Abel-Lidskii sense, we come to the conclusion that the concept can be formulated in the classical terms of the spectral theorem. Though, the spectral theorem for a sectorial operator has not been formulated even in the m-sectorial case, we can consider from this point of view a most simplified case related to the sectorial operator with a discrete spectrum. Thus, in accordance with the terms of the spectral theorem, we naturally arrive at the functional calculus for sectorial operators which is the main focus of this paper. Due to the functional calculus methods, we construct the operator class with the asymptotics more subtle then one of the power type.
2025
Volume 25- 16
Numéro 1 (Janvier 2025)2024
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Numéro 1 (Janvier 2024)2023
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Numéro 1 (Janvier 2023)2022
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Numéro spécial : AUS-ICMS 20202020
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Numéro 1 (Mai 2020)