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<p>We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the <i>d</i>-dimensional torus, and also when they are seen as infinite matrices acting on a discrete <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell ^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>ℓ</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators.</p>

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The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Horia D. Cornean,
  • Bernard Helffer,
  • Radu Purice

摘要

We study the structure of the fibre operators corresponding to periodic magnetic pseudo-differential operators having periodic magnetic potentials. We obtain explicit formulas for their distribution kernel, both when these fibres are seen as operators on the d-dimensional torus, and also when they are seen as infinite matrices acting on a discrete \(\ell ^2\) ℓ 2 space via a discrete Fourier transform. Moreover, using these distribution kernels we prove that the fibre operators are toroidal pseudo-differential operators.