Applications of APTARABOLDITALICO(APTARABOLDITALICp,APTARABOLDITALICq)†invariant distributions

Norbert Ortner and Peter Wagner

Mathematische Nachrichten, 2017, vol. 290, issue 17-18, 2995-3005

Abstract: In this sequel to the article , a criterion for the regularity of fundamental solutions of differential operators with positive symbol is proved in analogy to Hörmander's criteria, see . It implies that the temperate fundamental solution of the operator [∂,∂]2+1 is not regular. Furthermore, a formula for the convolution of two O(p,q)†invariant distributions is presented, and, finally, L. Schwartz' question on the surjectivity of linear partial differential operators with constant coefficients on the space OM is completely answered in the case of O(p,q)†invariant differential operators.

Date: 2017
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