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Norvidas Saulius - One of the best experts on this subject based on the ideXlab platform.

  • A note on analytic continuation of characteristic Functions
    2020
    Co-Authors: Norvidas Saulius
    Abstract:

    We derive necessary and sufficient conditions for a Continuous Bounded Function $f: R\to C$ to be a characteristic Function of a probability measure. The Cauchy transform $K_f$ of $f$ is used as analytic continuation of $f$ to the upper and lower half-planes in $C$. The conditions depend on the behavior of $K_f(z)$ and its derivatives on the imaginary axis in $C$. The main results are given in terms of completely monotonic and absolutely monotonic Functions.Comment: 6 page

Saulius Norvidas - One of the best experts on this subject based on the ideXlab platform.

  • on analytic continuation of characteristic Functions of probability measures
    Journal of Mathematical Analysis and Applications, 2012
    Co-Authors: Saulius Norvidas
    Abstract:

    Abstract We derive necessary and sufficient conditions for a Continuous Bounded Function f : R → C to be a characteristic Function of a probability measure. The Cauchy transform K f of f is used as analytic continuation of f to the upper and lower half-planes in C . The conditions depend on the behavior of K f ( z ) and its derivatives on the imaginary axis in C . The main results are given in terms of completely monotonic and absolutely monotonic Functions.

N V Demina - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic solution of the linearized morgenstern equation for small knudsen numbers
    Computational Mathematics and Modeling, 1992
    Co-Authors: N V Demina
    Abstract:

    is the unit vector running over the sphere f f in R 3, ~ l = g o (co, g '--~), ll '-~-g'--o (o, g '--g), 0 = -¢ (o, g'--.~), p = [g'--~i, B(p, 0) characterizes the law of molecular interaction, and h(x, y) is a Continuous Bounded Function that satisfies the conditions h(x, y) = h(y, x) _> 0, h(x, x) > 0. QM(F, F) is an operator that acts on the variables x and ~2 and is formally identical with the Boltzmann collision integral [2] if h = a(x y), where ~ is the Dirac delta-Function. In what follows we assume that the molecules interact as "rigid balls" and the Function B(p, 0) has the form

Ryan Peckner - One of the best experts on this subject based on the ideXlab platform.

  • m obius disjointness for homogeneous dynamics
    arXiv: Number Theory, 2015
    Co-Authors: Ryan Peckner
    Abstract:

    We prove Sarnak's Mobius disjointness conjecture for all unipotent translations on homogeneous spaces of real connected Lie groups. Namely, we show that if $G$ is any such group, $\Gamma\subset G$ a lattice, and $u\in G$ an Ad-unipotent element, then for every $x\in\Gamma\backslash G$ and every Continuous, Bounded Function $f$ on $\Gamma\backslash G$, the sequence $f(xu^{n})$ cannot correlate with the Mobius Function on average.

Wenhua Chen - One of the best experts on this subject based on the ideXlab platform.