Born-Jordan pseudodifferential operators with symbols in the Shubin classes

Cordero, Elena; de Gosson, Maurice; Nicola, Fabio

doi:10.1090/btran/16

Born-Jordan pseudodifferential operators with symbols in the Shubin classes
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by Elena Cordero, Maurice de Gosson and Fabio Nicola HTML | PDF

Trans. Amer. Math. Soc. Ser. B 4 (2017), 94-109

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 us to pass from Born-Jordan quantization to Weyl quantization and vice versa. In addition we state and prove some regularity and global hypoellipticity results.

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