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Spectral theory for a class of pseudodifferential operators

Published online by Cambridge University Press:  14 February 2012

E. A. Catchpole
E. A. Catchpole
Affiliation:
Royal Military College, Duntroon, Australia
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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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