ELYSEEVA, Julia, Peter ŠEPITKA a Roman ŠIMON HILSCHER. Comparative index and Hörmander index in finite dimension and their connections. Filomat. Faculty of Sciences and Mathematics, University of Nis, 2023, roč. 37, č. 16, s. 5243-5257. ISSN 0354-5180. Dostupné z: https://dx.doi.org/10.2298/FIL2316243E. |
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@article{2268721, author = {Elyseeva, Julia and Šepitka, Peter and Šimon Hilscher, Roman}, article_number = {16}, doi = {http://dx.doi.org/10.2298/FIL2316243E}, keywords = {Comparative index; Maslov index; Hörmander index; Lagrangian plane; Lagrangian path; Triple index; Wronskian}, language = {eng}, issn = {0354-5180}, journal = {Filomat}, title = {Comparative index and Hörmander index in finite dimension and their connections}, url = {https://www.pmf.ni.ac.rs/filomat-content/2023/37-16/37-16-6-19561.pdf}, volume = {37}, year = {2023} }
TY - JOUR ID - 2268721 AU - Elyseeva, Julia - Šepitka, Peter - Šimon Hilscher, Roman PY - 2023 TI - Comparative index and Hörmander index in finite dimension and their connections JF - Filomat VL - 37 IS - 16 SP - 5243-5257 EP - 5243-5257 PB - Faculty of Sciences and Mathematics, University of Nis SN - 03545180 KW - Comparative index KW - Maslov index KW - Hörmander index KW - Lagrangian plane KW - Lagrangian path KW - Triple index KW - Wronskian UR - https://www.pmf.ni.ac.rs/filomat-content/2023/37-16/37-16-6-19561.pdf N2 - 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. ER -
ELYSEEVA, Julia, Peter ŠEPITKA a Roman ŠIMON HILSCHER. Comparative index and Hörmander index in finite dimension and their connections. \textit{Filomat}. Faculty of Sciences and Mathematics, University of Nis, 2023, roč.~37, č.~16, s.~5243-5257. ISSN~0354-5180. Dostupné z: https://dx.doi.org/10.2298/FIL2316243E.
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