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<p>We consider the commutation relations between the Gauss–Weierstrass semigroup on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, generated by convolution with the complex Gaussian kernel, and monomial weights. We provide an explicit representation and a sharper estimate of the commutation relations with more concise proofs than those in previous works.</p>

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Remarks on the commutation relations between the Gauss–Weierstrass semigroup and monomial weights

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月10日

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  • Yi C. Huang,
  • Ryunosuke Kusaba,
  • Tohru Ozawa

摘要

We consider the commutation relations between the Gauss–Weierstrass semigroup on \(\mathbb {R}^{n}\) R n , generated by convolution with the complex Gaussian kernel, and monomial weights. We provide an explicit representation and a sharper estimate of the commutation relations with more concise proofs than those in previous works.