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To any function \(\displaystyle a(x,\xi ) = \sum _{|\alpha |\leq m} a_\alpha (x)\xi ^\alpha ,\quad a_\alpha \in \mathcal C_b^\infty (\mathbb {R}^n), \) we can associate a differential operator by setting \(\displaystyle ( \operatorname {\mathrm {Op}}(a)u)(x) := \sum _{|\alpha |\leq m} a_\alpha (x)D^\alpha u(x). \) The map \( \operatorname {\mathrm {Op}}\) thus defined is called a quantization map.

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    2025年

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  • Peter Hintz

摘要

To any function \(\displaystyle a(x,\xi ) = \sum _{|\alpha |\leq m} a_\alpha (x)\xi ^\alpha ,\quad a_\alpha \in \mathcal C_b^\infty (\mathbb {R}^n), \) we can associate a differential operator by setting \(\displaystyle ( \operatorname {\mathrm {Op}}(a)u)(x) := \sum _{|\alpha |\leq m} a_\alpha (x)D^\alpha u(x). \) The map \( \operatorname {\mathrm {Op}}\) thus defined is called a quantization map.