Page 1

Displaying 1 – 12 of 12

Showing per page

S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case

Josefina Alvarez, Martha Guzmán-Partida, Urszula Skórnik (2003)

Studia Mathematica

We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S’-convolutions. We characterize those tempered distribution that are S’-convolvable with the Poisson kernel in the Euclidean case and the product domain case. As an application...

Solutions to some nonlinear PDE's in the form of Laplace type integrals

Maria E. Pliś (2002)

Annales Polonici Mathematici

A nonlinear equation P ( D ) u = α u m in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.

Currently displaying 1 – 12 of 12

Page 1