Pseudo-Differential Operators on Manifolds with a Singular Boundary
The aim of this work is to describe new interesting examples of non-smooth manifolds and elliptic pseudo-differential operators acting in functional spaces on such manifolds. Fredholm properties for these operators are studied by factorization methods, and these are based on several complex variables.
KeywordsPseudo-differential operator Local representative Bochner operator Wave factorization
Mathematics Subject Classification (2010)Primary 47G30; Secondary 32A07
This work was supported by the State contract of the Russian Ministry of Education and Science (contract No 1.7311.2017/B).
- 5.R.B. Melrose, Pseudodifferential operators, corners and singular limits. In Proceeding of the International Congress of Mathematicians, 21–29 August 1990, Kyoto, Japan, ed. by Satake, vol. I (Springer, Tokyo, 1991), pp. 217–234Google Scholar
- 6.S. Moroianu, V. Nistor, Index and homology of pseudodifferential operators on manifolds with boundary. In Perspectives in Operator Algebras and Mathematical Physics. Theta Series in Advanced Mathematics, vol. 8 (Theta, Bucharest, 2008), pp. 123–148Google Scholar
- 9.I.B. Simonenko, A local method in the theory of translation invariant operators and their envelopings (in Russian) (CVVR Publishing, Rostov on Don, 2007)Google Scholar
- 14.V.B. Vasilyev, Pseudo differential equations on manifolds with non-smooth boundaries. In Differential and Difference Equations and Applications, ed. by S. Pinelas et al. Springer Proceedings in Mathematics & Statistics, vol. 47 (Birkhäuser, Basel, 2013), pp. 625–637Google Scholar
- 16.V.S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables (Dover Publications, Mineola, 2007)Google Scholar