Accession Number : AD0664473

Title :   A GENERALIZATION OF BERNSTEIN'S THEOREM AND A DIFFERENTIAL INVERSION FORMULA.

Descriptive Note : Technical rept.,

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Studden,William J.

Report Date : DEC 1967

Pagination or Media Count : 27

Abstract : A function phi(t) is called completely momotone (CM) on (o, infinity) if (-1) raised to the nth power phi(t) = or > o, n = 0, 1,... and t > o. Bernstein's theorem states that a function phi is CM if and only if phi is the Laplace transform of a measure on (o, infinity). Moreover the generating measure can be obtained from phi by applying a sequence of differential operators to phi. These two results are generalized to the case where (-1) raised to the nth power phi(t) = or > o, n = 0,1,... is replaced by an infinite sequence of differential inequalities of a special type. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), THEOREMS), MEASURE THEORY, INTEGRAL TRANSFORMS, OPERATORS(MATHEMATICS), CONVEX SETS, EXPONENTIAL FUNCTIONS, SEQUENCES(MATHEMATICS), INEQUALITIES, BOUNDARY VALUE PROBLEMS, CONVERGENCE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE