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Dissipative extension theory for linear relations

Institution:	2. Fenomenos Nonlineales y Mecánica (FENOMEC), Department of Mathematics and Mechanics, Instituto de Investigación en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, 01000 México D.F., Mexico;3. School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland, UK;1. Fenomenos Nonlineales y Mecánica (FENOMEC), Department of Mathematics and Mechanics, Instituto de Investigacion en Matemáticas Aplicadas y Sistemas, Universidad Nacional Autónoma de México, 01000 México D.F., Mexico;2. School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, New South Wales, 2522, Australia;3. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3FD, Scotland, UK;1. Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F., Mexico;2. School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia

Abstract:	This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the properties of dissipative relations are proven. Finally, we deal with the spectral properties of dissipative extensions of dissipative relations and provide results concerning particular realizations of this general setting.

Keywords:	Closed linear relations Dissipative extensions Nondensely defined operators
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