Operators Commuting with Translation by One — Part I

Representation Theorems

by David C. McGarvey

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A representation of operators in L#(<>) which commute with translation by one in terms of L#(0, 1) operator valued functions of <>. In a subsequent study, this representation is used to employ perturbation techniques, heretofore applicable only to operators with compact ret ret resolvents, to nonself adjoint differential operators with periodic coefficients on L#(<>), and to give conditions on the coefficients of these operators which ensure that they be spectral (completely reducible) even though they have continuous spectrum.

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