Excerpt from Some Absolutely Continuous Operators I
Most likely these conditions could be established for a wider class of operators, e.g. For the operator -a q, A being the Laplacian and the function q satisfying the povsner-ikebe condition Another example could be the operator M K, M being the multiplication operator and K satisfying a gentleness condition introduced by Friedrichs or a condition of partial gentleness introduced by the author, else where At present, however, we are not concerned with these questions.
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