Sur les fonctions absolument monotones

By S. Bernstein. 1929

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, background): “By construction, ϕ ′ ( D ) in (10) coincides with the class of completely mono-tonic functions f ( D ) obeying ( 1) n f ( n ) ( D ) ≥ 0 (Bernstein 1929).”
Properties of hierarchical Archimedean copulas (2013, background): “From Bernstein’s Theorem ([2]) it follows that each 2 L is the Laplace transform of some distribution function.”
Hyperbolicity and stable polynomials in combinatorics and probability (2012, unknown): “This result is the Bernstein–Widder Theorem [Ber28].”
Stieltjes-Pick-Bernstein-Schoenberg and their connection to complete monotonicity (2007, background): “It is less obvious that C is closed under pointwise convergence, but follows from the famous theorem of Bernstein proved in [17]: Theorem 1.”
Stationary covariances associated with exponentially convex functions (2003, background): “Bernstein (1929), Widder (1934; 1946, pp. 273 and 275) and Devinatz (1955) showed that a continuous function is exponentially convex if and only if it is of the form ł(s) ¼ ð er s dF(r), s 2 Rd , (5) where F is a non-negative finite measure on Rd and where the integral converges for all s.”
New Trends in General Variational Inequalities (2020, background): “Exponentially convex functions have appeared significant generalization of the convex functions, the origin of which can be traced back to Bernstein [16].”
Exponential convexity, positive semi–definite matrices and fundamental inequalities (2010, background): “This is a sub-class of convex functions introduced by Bernstein in [7] (see also [1], [20], [21]).”
COMPLETELY AND ALTERNATINGLY HYPEREXPANSIVE OPERATORS (2000, unknown): “with ak > 0 (see [ 10 ], and [25], Chapter IV, Theorem 3a).”
Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications (2019, methodology): “References 1.”