Problems of the Spectral Theory of Non Self Adjoint Operators
AIR FORCE SYSTEMS COMMAND WRIGHT-PATTERSON AFB OH FOREIGN TECHNOLOGY DIVISION
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The class of non self adjoint operators, for which the unconditionally converging expansion of the eigenfunctions is correct, has not yet been fully defined for example, it is not known whether ellipital differential operators with partial derivatives belong to this class. However, it is now clear that the spectral expansion converging on the norm is not a necessary characteristic of the general linear operator. Apparently, further development of the theory will be achieved by establishing the generalized spectral expansion. It is noted that considerable material has been accumulated in the theory of non self adjoint problems, and it is characteristic that in recent years the theory has been supplemented with a number of new and important studies. Successes have been particularly great in the area of operators with discrete spectrum. The first three sections discuss this theme.
- Theoretical Mathematics