A generalization of Douglis-Nirenberg elliptic operators

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Abstract

It is well known that the composition of two elliptic differential operators of orders ω and ω′ is again an elliptic operator of order ω+ω′. This fact is not true for the composition of two multi-order systems elliptic in the sense of Douglis and Nirenberg. We consider a new more general class of multi-order pseudodifferential operators. This class of multi-order essentially elliptic operators is closed with respect to the composition, coordinate and basis transformation. Moreover, every multi-order essentially elliptic operator has a parametrix belonging to the class and therefore is a Fredholm operator. Bibliography: 5 titles.

Original languageEnglish
Pages (from-to)472-481
Number of pages10
JournalJournal of Mathematical Sciences
Volume189
Issue number3
DOIs
StatePublished - Mar 2013

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Applied Mathematics

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