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An Information-Theoretic Analysis of High-Frequency Load Disaggregation. [PDF]
Entropy (Basel)Rodrigues GAP +4 more
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Completely monotonic functions
Integral Transforms and Special Functions, 2001In 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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Logarithmically completely monotonic functions and applications
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Senlin Guo
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Some Absolutely Monotonic and Completely Monotonic Functions
SIAM Journal on Mathematical Analysis, 1974The 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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Some classes of completely monotonic functions, II
The Ramanujan Journal, 2006[For part I see Ann. Acad. Sci. Fenn., Math. 27, No. 2, 445--460 (2002; Zbl 1021.26002).] A function \(f:(0,\infty )\rightarrow \mathbb{R}\) is said to be completely monotonic if \((-1)^{n}f^{(n)}(x)\geq 0\) for all \(x>0\) and \(n=0,1,2,\dots\) The authors present some new classes of completely monotonic functions.
Alzer, Horst, Berg, Christian
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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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A Property of completely monotonic functions
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1987AbstractA non-negative function f(t), t > 0, is said to be completely monotonic if its derivatives satisfy (-1)n fn (t) ≥ 0 for all t and n = 1, 2, …, For such a function, either f(t + δ) / f(t) is strictly increasing in t for each δ > 0, or f(t) = ce-dt for some constants c and d, and for all t. An application of this result is given.
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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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APPROXIMATION OF AND BY COMPLETELY MONOTONE FUNCTIONS
The ANZIAM Journal, 2019We investigate convergence in the cone of completely monotone functions. Particular attention is paid to the approximation of and by exponentials and stretched exponentials. The need for such an analysis is a consequence of the fact that although stretched exponentials can be approximated by sums of exponentials, exponentials cannot in general be ...
R. J. LOY, R. S. ANDERSSEN
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