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

• Autorzy: Josefina Alvarez , Martha Guzmán-Partida , Urszula Skórnik
• Języki publikacji: EN

Abstrakty

EN

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 of our results we prove that every integrable distribution on ℝⁿ has a harmonic extension to the upper half-space $ℝ₊^{n+1}$.

Kategorie tematyczne

• 46F10: Operations with distributions
• 46F12: Integral transforms in distribution spaces
• 46F05: Topological linear spaces of test functions, distributions and ultradistributions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 2
• Strony: 143-163

Daty

wydano

2003

Twórcy

autor

Josefina Alvarez

• Department of Mathematics, New Mexico State University, Las Cruces, NM 88003, U.S.A.

autor

Martha Guzmán-Partida

• Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Sonora 83000, México

autor

Urszula Skórnik

• Warsaw University of Agriculture, Nowoursynowska 166, 02-787 Warszawa, Poland

Identyfikatory

DOI

10.4064/sm156-2-5