A CONDITION FOR THE DISCRETENESS OF THE NEGATIVE SPECTRUM OF THE SCHROEDINGER OPERATOR,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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Let H be a symmetric operator with dense domain of definition in a Hilbert space. Let H be its Friedrichs self-adjoint extension. The author gives necessary and sufficient conditions for the operator H to be bounded below and for the operator H to have a negative discrete spectrum theorem 1. He then uses theorem 1 to extend the region of application of the criteria of discreteness of the negative spectrum of the Schrodinger operator theorem 2, which was previously deduced by I. M. Glazman and also by A. Persson. However, in contrast to Persson the class of operators is not restricted by the requirement that the potential be bounded below at infinity.
- Theoretical Mathematics