Fredholm inversion around a singularity: Application to autoregressive time series in Banach space

Autor:	Won-Ki Seo
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	operator pencils analytic fredholm theorem linear time-invariant dynamical systems granger-johansen representation theorem Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 31, Iss 8, Pp 4925-4950 (2023)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2023252?viewType=HTML
Popis:	This paper considers inverting a holomorphic Fredholm operator pencil. Specifically, we provide necessary and sufficient conditions for the inverse of a holomorphic Fredholm operator pencil to have a simple pole and a second order pole. Based on these results, a closed-form expression of the Laurent expansion of the inverse around an isolated singularity is obtained in each case. As an application, we also obtain a suitable extension of the Granger-Johansen representation theorem for random sequences taking values in a separable Banach space. Due to our closed-form expression of the inverse, we may fully characterize solutions to a given autoregressive law of motion except a term that depends on initial values.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/49196945708e4354845a73fe846b69ae Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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