
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