Some Properties of the Cauchy Function.
R. E. Gibson Library bulletin translation series,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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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
- Theoretical Mathematics