Journals / Turkish Journal of Mathematics / 2011 / Cilt: 35 - Sayı: 4
Multi-dimensional Weiss operators
- Pages
- 687–694
- DOI
- —
Abstract
We present a solution of the Weiss operator family generalized for the case of Rd and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation with the generalized Weiss operators. We illustrate the significance of our approach through several examples of both linear and non-linear partial differential equations.
Özet
We present a solution of the Weiss operator family generalized for the case of Rd and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a subset of null class functions for a partial differential equation with the generalized Weiss operators. We illustrate the significance of our approach through several examples of both linear and non-linear partial differential equations.