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Elliptic theory on manifolds with corners. I: Dual manifolds and pseudodifferential operators. (English) Zbl 1205.58017
Burghelea, Dan (ed.) et al., $$C^*$$-algebras and elliptic theory II. Selected papers of the international conference, Bȩdlewo, Poland, January 2006. Basel: Birkhäuser (ISBN 978-3-7643-8603-0/hbk). Trends in Mathematics, 183-206 (2008).
Summary: In this first part of the paper, we define a natural dual object for manifolds with corners and show how pseudodifferential calculus on such manifolds can be constructed in terms of the localization principle in $$C^*$$ algebras. In the second part [ibid., 207–226 (2008; Zbl 1205.58018)], these results will be applied to the solution of Gelfand’s problem on the homotopy classification of elliptic operators for the case of manifolds with corners.
For the entire collection see [Zbl 1134.58002].

##### MSC:
 58J40 Pseudodifferential and Fourier integral operators on manifolds 58J05 Elliptic equations on manifolds, general theory 47L15 Operator algebras with symbol structure 35S35 Topological aspects for pseudodifferential operators in context of PDEs: intersection cohomology, stratified sets, etc. 46L05 General theory of $$C^*$$-algebras