Optimal codomains for the Laplace operator and the product Laplace operatorReport as inadecuate




Optimal codomains for the Laplace operator and the product Laplace operator - Download this document for free, or read online. Document in PDF available to download.

Journal of Function Spaces and Applications - Volume 5 2007, Issue 3, Pages 269-285



Department of Mathematics, New Mexico State University, Las Cruces, New Mexico 88003, USA

Department of Mathematics, Sul Ross State University, Alpine, Texas 79832, USA

Received 1 May 2006

Academic Editor: Hans Triebel

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An optimal codomain for an operator P ∂ with fundamental solution E, is a maximal space of distributions T for which it is possible to define the convolution E*T and thus to solve the equation P ∂S=T. We identify optimal codomains for the Laplace operator in the Euclidean case and for the product Laplace operator in the product domain case. The convolution is understood in the sense of the S′-convolution.





Author: Josefina Alvarez and Lloyd Edgar S. Moyo

Source: https://www.hindawi.com/



DOWNLOAD PDF




Related documents