Explicit fundamental Solutions of Some Second Order Differential Operators

LINDA SAAL; ISOLDA CARDOSO

COLLOQUIUM MATHEMATICUM

Polish Academy of Sciences

Año: 2012 vol. 129 p. 263 - 288

0010-1354

I think that this is quite an interesting piece of mathematics. The au- thors consider the Heisenberg groups and the quaternionic Heisenberg groups and endow them with a scalar product with a non trivial sig- nature on the complement of the centre. Then they compute explicitly the fundamental solution of some second order dierential operators dened on these groups and associated to these scalar product. The result obtained are interesting and new. However, in my opinion, the paper could be considerably improved if, for instance, the author wrote a more extensive introduction motivating better their results and making an eort to explain the general strategy of the argument. In addition, I would like to suggest to the authors some small corrections, that are contained in the enclosed PDF le. Based on these reasons, I think that the paper under review, after some improvements, is good enough to be published in Colloquium Mathematicum.