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Friedrichs extension and essential spectrum of systems of differential operators of mixed order

✍ Scribed by Tobias Kusche; Reinhard Mennicken; Manfred Möller

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
226 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

A general construction for the Friedrichs extension of symmetric semi‐bounded block operators

with not necessarily bounded entries, acting in the product of Hilbert spaces has been given by Konstantinov and Mennicken via the form

There the entry A was assumed to be essentially self‐adjoint. Here it will be shown that the result remains true if A is only symmetric and that the closability of γ~μ~ follows from the semiboundedness of L ~0~. This will be applied to a 2 × 2 system of singular mixed‐order differential equations satisfying the quasi‐regularity condition, thus enabling us to give a much simpler calculation for the essential spectrum than in papers by Hardt, Mennicken, Naboko and Faierman, Mennicken, Möller, respectively, for a related 3 × 3‐system. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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