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Completely monotone functions on lie semigroups
Ukrainian Mathematical Journal, 2000A 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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Differential Approximation of Completely Monotonic Functions
SIAM Journal on Numerical Analysis, 1981The various differential approximation schemes for producing an exponential sum approximation to a given function F are placed within a common mathematical framework, and localization theorems are established in the important case where F is completely monotonic. The replacement of the least squares minimization by a Galerkin orthogonalization leads to
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Logarithmically completely monotonic functions and applications
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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\(L^p\) approximation of completely monotone functions
J. Approx. Theory, 2019A function \(f : [0,\infty) \to [0,\infty)\) is called completely monotone, if \(f\in C[0, \infty) \cap C^\infty(0,\infty)\) and satisfies \((-1)^n f^{(n)}(t)\ge 0\) (\(t>0, \, n=0,1.\dots\)). In the paper under review the authors prove that any completely monotone \(L^p\) function on \([0,\infty)\) is \(\|\cdot\|_p\) limit of a sequence of Dirichlet ...
R. J. Loy, Robert S. Anderssen
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Some Norm Inequalities for Completely Monotone Functions
SIAM Journal on Matrix Analysis and Applications, 2000Summary: Let \(A\), \(B\) be \(n\times n\) complex positive semidefinite matrices, and let \(f\) be a completely monotone function on \([0,\infty)\). We prove that \(2|||f(A+ B)|||\leq |||f(2A)+ f(2B)|||\) for all unitarily invariant norms \(|||\cdot |||\).
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A Completely Monotonic Function: 11140
The American Mathematical Monthly, 2006Walther Janous, Rolf Richberg
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On Completely Monotonic and Related Functions
2014We deal with several classes of functions, such as, completely monotonic functions, absolutely monotonic functions, logarithmically completely monotonic functions, Stieltjes functions, and Bernstein functions. We give several interesting relations among theses classes of functions as well as various examples and applications.
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Logarithmically completely monotonic functions related to the q-gamma function and its applications
Analysis and Mathematical Physics, 2022Khaled Mehrez +2 more
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A completely monotonic function involving the tri-gamma function and with degree one
Applied Mathematics and Computation, 2012Bai-Ni Guo, Feng Qi
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