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Comparative index and Hörmander index in finite dimension and their connections

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ELYSEEVA Julia ŠEPITKA Peter ŠIMON HILSCHER Roman

Rok publikování 2023
Druh Článek v odborném periodiku
Časopis / Zdroj Filomat
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www https://www.pmf.ni.ac.rs/filomat-content/2023/37-16/37-16-6-19561.pdf
Doi http://dx.doi.org/10.2298/FIL2316243E
Klíčová slova Comparative index; Maslov index; Hörmander index; Lagrangian plane; Lagrangian path; Triple index; Wronskian
Popis In this paper we prove new relations between the comparative index and the Hörmander index (and the Maslov index) in the finite dimensional case. As a main result we derive an algebraic formula for calculating the Hörmander index of four given Lagrangian planes as a difference of two comparative indices involving certain transformed Lagrangian planes, or as a combination of four comparative indices. This result is based on a generalization of the comparison theorem for the Maslov index involving three Lagrangian paths. In this way we contribute to the recent efforts in the literature (by Zhou, Wu, Zhu in 2018 and by Howard in 2021) devoted to an efficient calculation of the Hörmander index in this finite dimensional case.
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