Born-jordan Pseudodifferential Operators with Symbols in the Shubin Classes
نویسندگان
چکیده
We apply Shubin’s theory of global symbol classes Γρ 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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