Journal of Mathematical Physics, Analysis, Geometry
2017, vol. 13, No 3, pp. 205-241   https://doi.org/10.15407/mag13.03.205     ( to contents , go back )
https://doi.org/10.15407/mag13.03.205

On m-Sectorial Extensions of Sectorial Operators

Yury Arlinskii and Andrey Popov

Volodymyr Dahl East Ukrainian National University, 59-a Central Ave., Severodonetsk, 93400, Ukraine
E-mail: yury.arlinskii@gmail.com, andrey.b.popov@gmail.com

Received December 23, 2015, revised February 10, 2016

Abstract

We study maximal sectorial extensions of an arbitrary closed densely defined sectorial operator. In particular, abstract boundary conditions for these extensions are obtained. The results are applied for the parametrization of all m-sectorial extensions of a nonnegative symmetric operator in a planar model of two-point interactions.

Mathematics Subject Classification 2000: 47A20, 47B25, 47B44, 47A06, 47A07, 82B23.
Key words: sectorial operator, accretive operator, Friedrichs extension, Krein-von Neumann extension, boundary pair, boundary triplet.

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