Results 221 to 230 of about 9,662 (250)

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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A Property of completely monotonic functions

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1987
AbstractA 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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A Note on Completely and Absolutely Monotone Functions

Canadian Mathematical Bulletin, 1982
AbstractThe solutions of a certain class of first order linear differential equations are shown to be either completely or absolutely monotone depending on the nature of its coefficients. This is a simple theorem which is used to deduce a number of new and interesting results dealing with the complete and absolute monotonicity of functions.
Mahajan, Arvind, Ross, Dieter K.
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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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Differential Approximation of Completely Monotonic Functions

SIAM Journal on Numerical Analysis, 1981
The 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, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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\(L^p\) approximation of completely monotone functions

J. Approx. Theory, 2019
A 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, 2000
Summary: 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, 2006
Walther Janous, Rolf Richberg
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Completely monotone functions

2009
Ward Cheney, Will Light
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