Complex symmetric differential operators on Fock space

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:265

Article

Pham Viet Hai¹  Putinar, Mihai^2,3 

[1] Natl Univ Singapore, Singapore, Singapore

[2] Univ Calif Santa Barbara, Santa Barbara, CA 93106 USA

[3] Newcastle Univ, Newcastle Upon Tyne, Tyne & Wear, England

关键词: Fock space;    Differential operator;    Conjugation;    Complex symmetric operator;    Self-adjoint operator;    Point spectrum;   

DOI  :  10.1016/j.jde.2018.06.003

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free