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A uniqueness theorem in the inverse spectral theory of a certain higher-order ordinary differential equation using Paley-Wiener methods

Andersson, Erik LU (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)
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author
organization
publishing date
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
2007-08-02 10:48:58
date last changed
2017-01-01 04:39:16
@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},
  volume       = {72},
  year         = {2005},
}