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Complex symmetric differential operators on Fock space

Lookup NU author(s): Emeritus Professor Mihai Putinar

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Abstract

© 2018 Elsevier Inc. The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modeling and experimenting harmonic analysis, quantum mechanics or spectral analysis phenomena. This space of entire functions carries a three parameter family of canonical isometric involutions. We characterize the linear differential operators acting on Fock space which are complex symmetric with respect to these conjugations. In parallel, as a basis of comparison, we discuss the structure of self-adjoint linear differential operators. The computation of the point spectrum of some of these operators is carried out in detail.

Publication metadata

Author(s): Hai PV, Putinar M

Publication type: Article

Publication status: Published

Journal: Journal of Differential Equations

Year: 2018

Volume: 265

Issue: 9

Pages: 4213-4250

Print publication date: 05/11/2018

Online publication date: 19/06/2018

Acceptance date: 02/04/2018

Date deposited: 14/06/2018

ISSN (print): 0022-0396

ISSN (electronic): 1090-2732

Publisher: Academic Press Inc.

URL: https://doi.org/10.1016/j.jde.2018.06.003

DOI: 10.1016/j.jde.2018.06.003

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