Multi-dimensional Weiss operators

Details Multi-dimensional Weiss operators Multi-dimensional Weiss operators

2012-02-08

arxiv.org/abs/1202.1721v1

Turkish Journal of Mathematics, vol. 35 (2011), pp. 687-694

Mathematics

Analysis of PDEs

12 pages, already published in Turkish Journal of Mathematics

Scientific paper

10.3906/mat-1006-404

We present a solution of the Weiss operator family generalized for the case of $\mathbb{R}^{d}$ and formulate a d-dimensional analogue of the Weiss Theorem. Most importantly, the generalization of the Weiss Theorem allows us to find a sub-set 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.

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