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Gentle Perturbations of with Application to

Published online by Cambridge University Press:  20 November 2018

N. A. Derzko
N. A. Derzko*
Affiliation:
University of Toronto, Toronto, Ontario
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The theory of gentle perturbations was introduced by Friedrichs [3] as a tool to study the perturbation theory of the absolutely continuous spectrum of a self-adjoint operator H 0 and developed in an abstract form by Rejto [7; 8]. Two examples of gentle structures are well knowTn. In the first of these, the gentle operators have Hölder continuous complex or operator-valued kernels, and in the second, the kernels are Fourier transforms of L 1 functions [4].

The gentle structure has traditionally been verified in the case when H 0 is in its spectral representation, that is, when H 0 is the simple differentiation operator. This is not the natural setting for the second example mentioned above where one should consider the simple differentiation operator in a suitable L 2-space and perturbations with L 1 kernels.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 5 , 01 October 1970 , pp. 1055 - 1070
Copyright
Copyright © Canadian Mathematical Society 1970

References

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