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<p>Using Weyl calculus, it is established that the pair of evolution equations generated by a one-parameter diffusion semigroup in Bargmann–Fock and Gaussian spaces is intertwined by Gauss and Segal–Barman transforms. Their integral representations via Weyl kernels in these spaces on complex and real <i>n</i>-dimensional spaces are presented. For both cases, the infinitesimal generators are explicitly calculated. Solution formulas of initial value problems for appropriate pair of diffusion equations are found. In the case of fractional diffusion equations with jumping inhomogeneity, their solutions reduce to the Volterra integral equations.</p>

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Intertwined pair of diffusion equations generated by noncommutative Weyl calculus

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月18日

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  • Oleh Lopushansky

摘要

Using Weyl calculus, it is established that the pair of evolution equations generated by a one-parameter diffusion semigroup in Bargmann–Fock and Gaussian spaces is intertwined by Gauss and Segal–Barman transforms. Their integral representations via Weyl kernels in these spaces on complex and real n-dimensional spaces are presented. For both cases, the infinitesimal generators are explicitly calculated. Solution formulas of initial value problems for appropriate pair of diffusion equations are found. In the case of fractional diffusion equations with jumping inhomogeneity, their solutions reduce to the Volterra integral equations.