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Monotone completeness and convergence theorem

Monotone completeness and convergence theorem
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Delta Complete Monotonicity and Completely Monotonic Degree on Time Scales

Bulletin of the Malaysian Mathematical Sciences Society, 2023
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Zhong-Xuan Mao, Jing-Feng Tian
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Some Absolutely Monotonic and Completely Monotonic Functions

SIAM Journal on Mathematical Analysis, 1974
The functions $(1 - r)^{ - 2|\lambda |} (1 - 2xr + r^2 )^{ - \lambda } $ are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for $ - 1 \leqq x \leqq 1$. One consequence is a simple proof of Kogbetliantz’s theorem on positive Cesaro summability for ultraspherical series, [7].
Askey, Richard, Pollard, Harry
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Completely monotonic functions

Integral Transforms and Special Functions, 2001
In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [1, p.450], for example, that a function w is the Laplace transform of an infinitely divisible probability distribution on ...
K.S. Miller, S.G. Samko
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Completely Monotonic Fredholm Determinants

2020
A functionf(x) is called completely monotonic if (−1)mf(m)(x) > 0. In random matrix theory when the associated orthogonal polynomials have Freud weights, it is known that the expectation of having m eigenvalues of a random Hermitian matrix in an interval is a multiple of (−1)m times the m-th derivative of a Fredholm determinant at λ = 1.
Mourad E. H. Ismail, Ruiming Zhang
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Complete monotonicity and diesel fuel spray

The Mathematical Intelligencer, 2000
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Grinshpan, Arcadii Z., Ismail, Mourad E. H., Milligan, David L.   +2 more
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DYNAMIC ACTIONS ON MONOTONE COMPLETE FACTORS

The Quarterly Journal of Mathematics, 1993
Recall that for \(A\) a unital, monotone complete \(C^*\)-algebra, \(G_ 1\) and \(G_ 2\) countably infinite groups, and \(\alpha_ 1\), \(\alpha_ 2\) actions of \(G_ 1\) and \(G_ 2\), respectively, as \(*\)-automorphisms of \(A\), the actions \(\alpha_ 1\) and \(\alpha_ 2\) are called weakly equivalent if there exists an isomorphism of the monotone ...
Saitô, Kazuyuki, Wright, J. D. Maitland
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Monotone Completions of the Fermion Algebra

The Quarterly Journal of Mathematics, 2002
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Saitô, Kazuyuki, Wright, J. D. Maitland
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Completely monotone functions on lie semigroups

Ukrainian Mathematical Journal, 2000
A totally monotone function on a semigroup \(S\) was defined by \textit{A. Devinatz} and \textit{A. E. Nussbaum} [Duke Math. J. 28, 221-237 (1961; Zbl 0118.11201)] as a function satisfying certain difference inequalities. The author shows that the latter are equivalent to some differential inequalities if \(S\) is a Lie semigroup.
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Generalized Gamma convolutions and complete monotonicity

Probability Theory and Related Fields, 1990
Let \({\mathcal C}\) be the class of pdf's f on (0,\(\infty)\) such that, for each \(u>0\), f(uv)f(u/v) is completely monotone as a function of \(w=v+v^{-1}\). This class includes many familiar pdf's and is closed with respect to multiplication and division of independent rv's.
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