Related papers: On the Laplace transform
The aim of this work is to prove inverse formulas for Laplace transform on semilattices of open-and-compact sets in a both discrete and non-discrete cases. These are partial answers to a question posed by Yu.~I.~Lyubich.
It is widely claimed that the quantile function is equivariant under increasing transformations. We show by a counterexample that this is not true (even for strictly increasing transformations). However, we show that the quantile function…
Let $T$ be an arbitrary operator bounded from $L^{p_0}(w)$ into $L^{p_0, \infty}(w)$ for every weight $w$ in the Muckenhoupt class $A_{p_0}$. It is proved in this article that the distribution function of $Tf$ with respect to any weight $u$…
We prove fourteen equivalent conditions for a set of timefrequency shifts on a lattice to be a frame for L^2. Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the…
Let $(\mu_{\alpha})$ be a net of Radon sub-probability measures on the real line, and $(t_{\alpha})$ be a net in $]0,+\infty[$ converging to 0. Assuming that the generalized log-moment generating function $L(\lambda)$ exists for all…
In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via…
The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the…
A popular and efficient discretization of evolutions involving the singular $p$-Laplace operator is based on a factorization of the differential operator into a linear part which is treated implicitly and a regularized singular factor which…
Let $F(y):=\displaystyle\int_t^TL(s, y(s), y'(s))\,ds$ be a positive functional, unnecessarily autonomous, defined on the space $ W^{1,p}([t,T]; \mathbb R^n)$ ($p\ge 1$) of Sobolev functions, possibly with prescribed one or two end point…
We study a transmission problem, in population dynamics, between two juxtaposed habitats. In each habitat, we consider a generalized diffusion equation composed by the Laplace operator and a biharmonic term. We consider that the…
Laplace's method is used to approximate intractable integrals in a statistical problems. The relative error rate of the approximation is not worse than $O_p(n^{-1})$. We provide the first statistical lower bounds showing that the $n^{-1}$…
A new generalized function space in which all Gelfand-Shilov classes $S^{\prime 0}_\alpha$ ($\alpha>1$) of analytic functionals are embedded is introduced. This space of {\it ultrafunctionals} does not possess a natural nontrivial topology…
Starting from the approach to the Laplacian with respect to coupling measures and undirected weighted graphs, we provide a setting for a general point of view for a Kirchhoff type divergence and a Laplace operators built on the trivial…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
In this paper, we generalized the known Laplace-transform final-value theorem. From our conclusion, one can deduce the existing results in [1, 3, 12]. By using final value theorem, we give a new proof that Caputo fractional differential…
Transition probabilities for a class of two level systems described by explicitly time dependent Hamiltonians are considered. Provided only that the approach to the infinite time limit is non-trivial falling at least as fast as 1/t for…
Let $(A,\mathscr{A},\mu)$ and $(B,\mathscr{B},\nu)$ be probability spaces, let $\mathscr{F}$ be a sub-$\sigma$-algebra of the product $\sigma$-algebra $\mathscr{A}\times\mathscr{B}$, let $X$ be a Banach space, and let $1< p,q< \infty$. We…
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition…
We construct a simple toy model and explicitly demonstrate that the Balance Function (BF) can become negative for some values of the rapidity separation and hence can not have any probabilistic interpretation. In particular, the BF can not…