We construct Almansi decompositions for a class of differential operators, which include powers of the classical Laplace operator, heat operator, and wave operator. The decomposition is given in a constructive way.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-5, author = {Guangbin Ren and Uwe K\"ahler}, title = {Almansi decompositions for polyharmonic, polyheat, and polywave functions}, journal = {Studia Mathematica}, volume = {173}, year = {2006}, pages = {91-100}, zbl = {1093.31001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-5} }
Guangbin Ren; Uwe Kähler. Almansi decompositions for polyharmonic, polyheat, and polywave functions. Studia Mathematica, Tome 173 (2006) pp. 91-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm172-1-5/