DOI: 10.3390/math14203799 ISSN: 2227-7390

Characteristic Function Operator

Leon Cohen
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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.

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