Complex symmetric differential operators on Fock space
Mathematical Physics
2018-03-14 v1 Complex Variables
math.MP
Abstract
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 modelling 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.
Cite
@article{arxiv.1803.04890,
title = {Complex symmetric differential operators on Fock space},
author = {Pham Viet Hai and Mihai Putinar},
journal= {arXiv preprint arXiv:1803.04890},
year = {2018}
}
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34 pages