A uniqueness theorem in the inverse spectral theory of a certain higherorder ordinary differential equation using PaleyWiener methods
(2005) In Journal of the London Mathematical Society 72(1). p.169184 Abstract
 The paper examines a higherorder 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 PaleyWiener 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 higherorder 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 PaleyWiener 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:
http://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
 00246107
 DOI
 10.1112/S0024610704005770
 language
 English
 LU publication?
 yes
 id
 78170b2114da46a8ab2af8a1d08917d8 (old id 226236)
 date added to LUP
 20070802 10:48:58
 date last changed
 20180107 05:32:00
@article{78170b2114da46a8ab2af8a1d08917d8, abstract = {The paper examines a higherorder 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 PaleyWiener 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 = {00246107}, language = {eng}, number = {1}, pages = {169184}, publisher = {Oxford University Press}, series = {Journal of the London Mathematical Society}, title = {A uniqueness theorem in the inverse spectral theory of a certain higherorder ordinary differential equation using PaleyWiener methods}, url = {http://dx.doi.org/10.1112/S0024610704005770}, volume = {72}, year = {2005}, }