A GENERALIZATION OF BERNSTEIN'S THEOREM AND A DIFFERENTIAL INVERSION FORMULA.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1967
- Accession Number
- AD0664473
Entities
People
- William J. Studden
Organizations
- Purdue University