Densities, Laplace Transforms and Analytic Number Theory

Some Applications of Laplace Transforms in Analytic Number Theory

Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...

A Century of Complex Tauberian Theory

Complex-analytic and related boundary properties of transforms give information on the behavior of pre-images. The transforms may be power series, Dirichlet series or Laplace-type integrals; the pre-images are series (of numbers) or functions. The chief impulse for complex Tauberian theory came from number theory. The first part of the survey emphasizes methods which permit simple derivations o...

Axisymmetric Problem of Thick Circular Plate with Heat Sources in Modified Couple Stress Theory

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in modified couple stress theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governi...

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

A note on the comparison between Laplace and Sumudu transforms