Gentle Perturbations of with Application to

Derzko, N. A.

Canadian journal of mathematics, Tome 22 (1970) no. 5, pp. 1055-1070

Résumé

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.

Détail

DOI : 10.4153/CJM-1970-122-7

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