Accession Number : AD0668000

Title :   FUNDAMENTAL THEOREMS ON THE EXTENSION OF HERMITIAN OPERATORS AND SOME OF THEIR APPLICATIONS TO THE THEORY OF ORTHOGONAL POLYNOMIALS AND TO THE PROBLEM OF MOMENTS,

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

Personal Author(s) : Krein,M. G. ; Krasnoselskii,M. A.

Report Date : 14 FEB 1968

Pagination or Media Count : 78

Abstract : Presented are various theorems on the extension of operators with a systematic use of a linear-fractional transformation of a linear operator. Also shown is that every Hermitian operator with dense domain of definition which has a spectral gap admits a self-adjoint extension and preserves the gap. The invariance of defect indices in the upper and lower half planes is proven for the case of arbitrary linear operators. Fundamental concepts dealing with linear operators in a Hilbert space are presented. Various examples appear throughout the paper showing the application of the derived theorems. They are taken from the theory of orthogonal polynomials and the problem of moments. (Author)

Descriptors :   (*OPERATORS(MATHEMATICS), THEOREMS), POLYNOMIALS, SEQUENCES(MATHEMATICS), TRANSFORMATIONS(MATHEMATICS), HILBERT SPACE, FUNCTIONAL ANALYSIS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE