Vol. 6, No. 1, 2013

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Resolvent estimates for elliptic quadratic differential operators

Michael Hitrik, Johannes Sjöstrand and Joe Viola

Vol. 6 (2013), No. 1, 181–196
Abstract

Sharp resolvent bounds for nonselfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.

Keywords
nonselfadjoint operator, resolvent estimate, spectrum, quadratic differential operator, FBI-Bargmann transform
Mathematical Subject Classification 2010
Primary: 15A63, 35P05, 47A10, 53D22
Milestones
Received: 23 September 2011
Revised: 29 November 2011
Accepted: 16 January 2012
Published: 1 June 2013
Authors
Michael Hitrik
Department of Mathematics
UCLA
Los Angeles 90095-1555
United States
Johannes Sjöstrand
IMB, Université de Bourgogne
9, Av. A. Savary, BP 47870
21078 Dijon
France
UMR 5584 CNRS
Joe Viola
Mathematical Sciences
Lund University
Box 118
SE-22100 Lund
Sweden