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Spectral theory for a class of pseudodifferential operators
Published online by Cambridge University Press: 14 February 2012
Synopsis
We investigate the spectral theory for a class of pseudodifferential operators which includes all constant coefficient differential operators, and also operators such as The operators considered are of the form Su(x) = Au(x)+q(x)u(x), where A is an operator which corresponds in the Fourier transform plane to a multiplication operator, and q(x) is a potential term. We prove an eigenfunction expansion theorem for S and derive some results concerning the spectrum of S.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 3 , 1977 , pp. 197 - 214
- Copyright
- Copyright © Royal Society of Edinburgh 1977
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