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<p>We study the product of the kernel functions of two pseudodifferential operators. In general, this product is not well-defined in the usual distribution sense. Using the regularization method in quantum field theory, we show that we can define this product for a class of pseudodifferential operators. Furthermore, we show that such a product again defines a pseudodifferential operator.</p>

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Renormalization and pseudodifferential operators

  • 期刊论文

  • 发表日期：

    2025年6月23日

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  • Keisuke Uchikoshi

摘要

We study the product of the kernel functions of two pseudodifferential operators. In general, this product is not well-defined in the usual distribution sense. Using the regularization method in quantum field theory, we show that we can define this product for a class of pseudodifferential operators. Furthermore, we show that such a product again defines a pseudodifferential operator.