A uniqueness theorem in the inverse spectral theory of a certain higher-order ordinary differential equation using Paley-Wiener methods
(2005) In Journal of the London Mathematical Society 72(1). p.169-184- Abstract
- The paper examines a higher-order ordinary differential equation of the form P[u]:= Sigma(j,k=0)(m) D(j)a(jk)D(k)u = gimel u, x is an element of [0, b), where D=i(d/dx), and where the coefficients a(jk), j, k is an element of [0,M], with a = 1, satisfy certain regularity conditions and are chosen so that the matrix (a(jk)) is hermitean. It is also assumed that m > 1. More precisely, it is proved, using Paley-Wiener methods, that the corresponding spectral measure determines the equation up to conjugation by a function of modulus 1. The paper also discusses under which additional conditions the spectral measure uniquely determines the coefficients a(jk), j, k E [0, m], J + k not equal 2m, as well as b and the boundary conditions at 0 and... (More)
- The paper examines a higher-order ordinary differential equation of the form P[u]:= Sigma(j,k=0)(m) D(j)a(jk)D(k)u = gimel u, x is an element of [0, b), where D=i(d/dx), and where the coefficients a(jk), j, k is an element of [0,M], with a = 1, satisfy certain regularity conditions and are chosen so that the matrix (a(jk)) is hermitean. It is also assumed that m > 1. More precisely, it is proved, using Paley-Wiener methods, that the corresponding spectral measure determines the equation up to conjugation by a function of modulus 1. The paper also discusses under which additional conditions the spectral measure uniquely determines the coefficients a(jk), j, k E [0, m], J + k not equal 2m, as well as b and the boundary conditions at 0 and at b (if any). (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/226236
- author
- Andersson, Erik LU
- organization
- publishing date
- 2005
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of the London Mathematical Society
- volume
- 72
- issue
- 1
- pages
- 169 - 184
- publisher
- Oxford University Press
- external identifiers
-
- wos:000231637500011
- scopus:33644611125
- ISSN
- 0024-6107
- DOI
- 10.1112/S0024610704005770
- language
- English
- LU publication?
- yes
- id
- 78170b21-14da-46a8-ab2a-f8a1d08917d8 (old id 226236)
- date added to LUP
- 2016-04-01 11:54:23
- date last changed
- 2022-01-26 19:59:26
@article{78170b21-14da-46a8-ab2a-f8a1d08917d8,
abstract = {{The paper examines a higher-order ordinary differential equation of the form P[u]:= Sigma(j,k=0)(m) D(j)a(jk)D(k)u = gimel u, x is an element of [0, b), where D=i(d/dx), and where the coefficients a(jk), j, k is an element of [0,M], with a = 1, satisfy certain regularity conditions and are chosen so that the matrix (a(jk)) is hermitean. It is also assumed that m > 1. More precisely, it is proved, using Paley-Wiener methods, that the corresponding spectral measure determines the equation up to conjugation by a function of modulus 1. The paper also discusses under which additional conditions the spectral measure uniquely determines the coefficients a(jk), j, k E [0, m], J + k not equal 2m, as well as b and the boundary conditions at 0 and at b (if any).}},
author = {{Andersson, Erik}},
issn = {{0024-6107}},
language = {{eng}},
number = {{1}},
pages = {{169--184}},
publisher = {{Oxford University Press}},
series = {{Journal of the London Mathematical Society}},
title = {{A uniqueness theorem in the inverse spectral theory of a certain higher-order ordinary differential equation using Paley-Wiener methods}},
url = {{http://dx.doi.org/10.1112/S0024610704005770}},
doi = {{10.1112/S0024610704005770}},
volume = {{72}},
year = {{2005}},
}