Applications of APTARABOLDITALICO(APTARABOLDITALICp, APTARABOLDITALICq)‐invariant distributions. Issue 17 (8th December 2017)

• Record Type: Journal Article
• Authors: Ortner, Norbert; Wagner, Peter
• Is Part Of: Mathematische Nachrichten. Volume 290:Issue 17/18(2017)
• Page Start: 2995
• Page End: 3005
• Publication Date: 2017-12-08
• Subjects: Convolution -- Fourier transform -- O(p, q)‐invariant differential operators -- regular fundamental solutions -- surjective differential operators on OM -- 35C05 -- 35D10 -- 35E05 -- 35M99 -- 42B10 -- 46F10 -- 46F12; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201700027
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: In this sequel to the article17, a criterion for the regularity of fundamental solutions of differential operators with positive symbol is proved in analogy to Hörmander's criteria, see9 12 . 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 O M is completely answered in the case of O ( p, q ) ‐invariant differential operators.