TY - JOUR

T1 - Asymptotics of determinants of 4-th order operators at zero

AU - Badanin, Andrey

AU - Korotyaev, Evgeny L.

N1 - Funding Information: A. Badanin was supported by the RFBR grant No 19‐01‐00094. E. Korotyaev was supported by the RSF grant No. 18‐11‐00032.

PY - 2020/2

Y1 - 2020/2

N2 - 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.

AB - 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.

KW - 34L25

KW - 47E05

KW - asymptotics

KW - fourth order operators

KW - Fredholm determinant

KW - INVERSE RESONANCE SCATTERING

KW - POLES

UR - http://www.scopus.com/inward/record.url?scp=85075481037&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/41cde84f-d8ce-3389-b01a-e339564d5d21/

U2 - 10.1002/mana.201800548

DO - 10.1002/mana.201800548

M3 - Article

AN - SCOPUS:85075481037

VL - 293

SP - 210

EP - 225

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 2

ER -