Accession Number : AD0673161

Title :   A CONDITION FOR THE DISCRETENESS OF THE NEGATIVE SPECTRUM OF THE SCHROEDINGER OPERATOR,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Zhislin,G. M.

Report Date : 27 MAY 1968

Pagination or Media Count : 11

Abstract : Let H be a symmetric operator with dense domain of definition in a Hilbert space. Let H* be its Friedrich's 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.

Descriptors :   (*OPERATORS(MATHEMATICS), HILBERT SPACE), POTENTIAL THEORY, FUNCTIONAL ANALYSIS, SEQUENCES(MATHEMATICS), CONVERGENCE, THEOREMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE