We present a solution of the Weiss operator family generalized for the case of 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 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.
BORİSENOK, SERGEY; ERKUT, MEHMET HAKAN; POLATOĞLU, YAŞAR; and DEMİRER, RÜŞTÜ MURAT
"Multi-dimensional Weiss operators,"
Turkish Journal of Mathematics: Vol. 35:
4, Article 8.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss4/8