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Asymptotics of determinants of 4‐th order operators at zero
Author(s) -
Badanin Andrey,
Korotyaev Evgeny L.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800548
Subject(s) - mathematics , fredholm determinant , zero (linguistics) , differential operator , zero order , perturbation (astronomy) , complex plane , order (exchange) , fredholm theory , mathematical analysis , half line , operator (biology) , line (geometry) , first order , analytic function , pure mathematics , ordinary differential equation , function (biology) , fredholm integral equation , differential equation , geometry , integral equation , philosophy , repressor , boundary value problem , linguistics , chemistry , biology , biochemistry , evolutionary biology , transcription factor , finance , economics , gene , quantum mechanics , physics
We consider fourth order ordinary differential operators on the half‐line and on the line, where the perturbation has compactly supported coefficients. The Fredholm determinant for this operator is an analytic function in the whole complex plane without zero. We describe the determinant at zero. We show that in the generic case it has a pole of order 4 in the case of the line and of order 1 in the case of the half‐line.