Accession Number : AD0770087

Title :   On the Generalization of the Volterra Principle of Inversion.

Descriptive Note : Interim technical rept.,

Corporate Author : MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB

Personal Author(s) : Porter,William A. ; DeSantis,Romano M.

Report Date : SEP 1973

Pagination or Media Count : 11

Abstract : In the article a linear operator, K, defined on a Hilbert space equipped with a chain of orthoprojectors is considered. It is proved that if K enjoys a particular property with respect to the chain of orthoprojectors, then the series the summation from n=0 to infinity of (K sup n) converges in the uniform operator norm. The proof uses purely algebraic techniques and does not require compactness of K. As such it is a significant generalization of the wellknown Volterra principle of inversion. (Author)

Descriptors :   (*Integral equations, *Hilbert space), Operators(Mathematics), Theorems

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE