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):

Report Date:

1971-02-16

Pagination or Media Count:

9.0

Abstract:

Let Kt,s be the Cauchy function of the linear equation g sup n Summation of g sub kty 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 it Kt, 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 non-oscillation interval, i.e. an interval in which any non-trivial solution of Eq. 1 has no more than n-1 zeros. The existence of the conditions of smoothness is not clarified. Criteria are given for the sign-preservation of Kt,s. Author

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE