Weinstein-type Segal–Bargmann transform and its applications to partial differential equations

Abstract

In this paper, we give some applications of the Weinstein-type Segal–Bargmann transform ${\mathcal{B}}_{\alpha }$ in the field of partial differential equations, such as the time-dependent Schrödinger equation and heat Cauchy problems associated with the Weinstein operator. The resolution of these types of problems is based on the techniques of the transmutation operators on the Weinstein-type Fock space ${\mathcal{F}}_{\alpha ,\ast }({\mathbb{C}}^d)$.

KEYWORDS:

• Weinstein-type Segal–Bargmann transform
• time-dependent Weinstein–Schrödinger equation
• time-dependent heat Cauchy problems

AMS SUBJECT CLASSIFICATIONS:

• 30H20
• 35Q41
• 44A20

Acknowledgments

The authors would like to thank the referee for the careful reading and editing of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).