Work

Characteristic Function Operator

Year: 2026

Type: article

Abstract: We define the characteristic function operator eiθA+iτB, where A and B are explicit functions of the operators x and D. Operators of this form arise in a wide range of applications, including quantum mechanics, evolution equations, and time–frequency analysis. We briefly review the historical development of the characteristic function operator and present a general method for evaluating its action on functions in both the spatial and Fourier domains. The method relies on solving the eigenvalue problem for θA+τB. A number of examples are presented. The method is then applied to the solution of evolution equations.

Source: Mathematics

DOI: 10.3390/math14203799

Author: Leon Cohen

Institution: Texas A&M University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Welch Foundation, Air Force Office of Scientific Research