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An inverse spectral theory of Gel'fand-Levitan-type for higher order differential operators

โœ Scribed by W. W. Zachary

Publisher
Springer
Year
1984
Tongue
English
Weight
408 KB
Volume
8
Category
Article
ISSN
0377-9017

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โœฆ Synopsis

An inverse spectral theory is presented for certain linear ordinary differential operators of arbitrary even order n which generalizes the Gel'fand-Levitan theory for Stu~m-Liouville operators. It is proved that the coefficients in these operators are uniquely determined by n -1 distinct spectral matrices. Our method of proof makes use of a transformation due to M.K. Fage which generalizes the Povzner-Levitan transformations for Sturm-Liouville operators

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โœ Vjacheslav Yurko ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 211 KB ๐Ÿ‘ 2 views

We study the inverse problem of recovering differential operators of the Orr -Sommerfeld type from the Weyl matrix. Properties of the Weyl matrix are investigated, and an uniqueness theorem for the solution of the inverse problem is proved.