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On the index of degenerate pseudodifferential operators on a closed curve
Author(s) -
Elschner Johannes
Publication year - 1982
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19821090108
Subject(s) - degenerate energy levels , mathematics , smoothness , pseudodifferential operators , sobolev space , index (typography) , mathematical analysis , class (philosophy) , plane (geometry) , pure mathematics , oblique case , principal part , geometry , computer science , physics , quantum mechanics , artificial intelligence , world wide web , linguistics , philosophy
Abstract We consider a class of degenerate classical pseudodifferential operators on a closed curve and compute their index in Sobolev spaces. The index is expressed as a winding number by means of the principal and the subprincipal symbol. Furthermore, applications to the smoothness of solutions and the degenerate oblique derivative problem in the plane are given.