EuDML | Browse

Let $S_{n}$ be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of $S_{n}$ which takes into account the influence of the roots of the equation $1 - \int_{ℝ} e^{s x} F (d x) = 0, F$ being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace transforms....

Analytical investigations of the Sudumu transform and applications to integral production equations.

Belgacem, Fethi bin Muhammed, Karaballi, Ahmed Abdullatif, Kalla, Shyam L. (2003)

Mathematical Problems in Engineering

Are linear algorithms always good for linear problems?

H. Wozniakowski, Arthur G. Werschulz (1986)

Aequationes mathematicae

Around Widder’s characterization of the Laplace transform of an element of $L^{\infty} (ℝ^{+})$

Jan Kisyński (2000)

Annales Polonici Mathematici

Let ϰ be a positive, continuous, submultiplicative function on $ℝ^{+}$ such that $l i m_{t \to \infty} e^{- ω t} t^{- α} ϰ (t) = a$ for some ω ∈ ℝ, α ∈ $\bar{ℝ^{+}}$ and $a \in ℝ^{+}$ . For every λ ∈ (ω,∞) let $ϕ_{λ} (t) = e^{- λ t}$ for $t \in ℝ^{+}$ . Let $L_{ϰ}^{1} (ℝ^{+})$ be the space of functions Lebesgue integrable on $ℝ^{+}$ with weight $ϰ$ , and let E be a Banach space. Consider the map $ϕ_{•} : (ω, \infty) ∋ λ \to ϕ_{λ} \in L_{ϰ}^{1} (ℝ^{+})$ . Theorem 5.1 of the present paper characterizes the range of the linear map $T \to T ϕ_{•}$ defined on $L (L_{ϰ}^{1} (ℝ^{+}); E)$ , generalizing a result established by B. Hennig and F. Neubrander for $ϰ (t) = e^{ω t}$ . If ϰ ≡ 1 and E =ℝ then Theorem 5.1 reduces to D. V. Widder’s characterization...

Associated transforms for solution of nonlinear equations.

Debnath, Joyati, Debnath, Narayan C. (1991)

International Journal of Mathematics and Mathematical Sciences

Asymmetric deformation of anisotropic porous bodies.

Chakraborty, Dilip, Chakraborty, Amitava (1984)

International Journal of Mathematics and Mathematical Sciences

Asymptotic behavior of Fourier-Laplace transform

Lars Hörmander (1993)

Journées équations aux dérivées partielles

Asymptotic Fourier and Laplace transformations for hyperfunctions

Michael Langenbruch (2011)

Studia Mathematica

We develop an elementary theory of Fourier and Laplace transformations for exponentially decreasing hyperfunctions. Since any hyperfunction can be extended to an exponentially decreasing hyperfunction, this provides simple notions of asymptotic Fourier and Laplace transformations for hyperfunctions, improving the existing models. This is used to prove criteria for the uniqueness and solvability of the abstract Cauchy problem in Fréchet spaces.