We apply Shubin's theory of global symbol classes $\Gamma_{\rho}^{m}$ to the Born-Jordan pseudodifferential calculus we have previously developed. This approach has many conceptual advantages, and makes the relationship between the conflicting Born-Jordan and Weyl quantization methods much more limpid. We give, in particular, precise asymptotic expansions of symbols allowing to pass from Born-Jordan quantization to Weyl quantization, and vice-versa. In addition we state and prove some regularity and global hypoellipticity results.

Born-Jordan Pseudo-Differential Operators with Symbols in the Shubin Classes

Elena Cordero;
2017-01-01

Abstract

We apply Shubin's theory of global symbol classes $\Gamma_{\rho}^{m}$ to the Born-Jordan pseudodifferential calculus we have previously developed. This approach has many conceptual advantages, and makes the relationship between the conflicting Born-Jordan and Weyl quantization methods much more limpid. We give, in particular, precise asymptotic expansions of symbols allowing to pass from Born-Jordan quantization to Weyl quantization, and vice-versa. In addition we state and prove some regularity and global hypoellipticity results.
2017
4
94
109
https://doi.org/10.1090/btran/16
Born-Jordan quantization, pseudodifferential operators, Shubin classes, Weyl quantization
Elena Cordero, Maurice de Gosson, Fabio Nicola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1660455
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