Extension theory for elliptic partial differential operators with pseudodifferential methods

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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 new results), namely to
the lower boundedness question, and the question of spectral asymptotics for
differences between resolvents.
Original languageEnglish
Title of host publicationOperator Methods for Boundary Value Problems
EditorsSeppo Hassi, Hendrik de Snoo, Franciszek Szafraniec
Number of pages38
Place of PublicationCambridge
PublisherCambridge University Press
Publication date2012
ISBN (Print)978-1-197-60611-1
Publication statusPublished - 2012
SeriesLondon Mathematical Society. Lecture Note Series

ID: 43665997