Extension theory for elliptic partial differential operators with pseudodifferential methods

Details Extension theory for elliptic partial differential operators with pseudodifferential methods Extension theory for elliptic partial differential operators with pseudodifferential methods

2010-08-05

arxiv.org/abs/1008.1081v3

Mathematics

Analysis of PDEs

26 pages, style changed to LaTeX, new material added at the end, to appear in the Lecture Notes Series of the London Math. Soc

Scientific paper

This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very useful here, not only as a formulational framework, but also for the solution of specific questions. We recall some elements of that theory, and show its application in several cases (including recent results), namely to the lower boundedness question, and the question of spectral asymptotics for differences between resolvents.

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