
Accession Number : AD0722205
Title : Some Properties of the Cauchy Function.
Descriptive Note : R. E. Gibson Library bulletin translation series,
Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
Personal Author(s) : Aliev,R. G. ; Ostroumov,V. V. ; Pak,S. A.
Report Date : 16 FEB 1971
Pagination or Media Count : 9
Abstract : Let K(t,s) be the Cauchy function of the linear equation (g sup n) = Summation of ((g sub k)(t)(y sup k)). (1) It is shown that if g sub k is summable in any interval, there are found n points s sub i such that the functions (y sub i)(t) = K(t, s sub i) (i = 1,...,n) are linearly independent. If g sub k is sufficiently smooth (e.g. the equation adjoint to (1) has continuous coefficients), the points s sub i can be chosen arbitrarily within the nonoscillation interval, i.e. an interval in which any nontrivial solution of Eq. (1) has no more than n1 zeros. The existence of the conditions of smoothness is not clarified. Criteria are given for the signpreservation of K(t,s). (Author)
Descriptors : (*DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), MATRICES(MATHEMATICS), SERIES(MATHEMATICS), INEQUALITIES, THEOREMS, USSR
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE