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<p>We consider a bicomplex analogue of the Landau Hamiltonian defined via its idempotent representation as a couple of the classical Landau Hamiltonians on two separate complex discs. We provide a complete characterization of its <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-eigenspaces when acting on the so-called bicomplex <i>p</i>-Hilbert space, which next employed to explore the common eigenfunction problem associated with the magnetic bc-Laplacian and its <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\dagger \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>†</mo> </math></EquationSource> </InlineEquation>-conjugate. The corresponding eigenspaces give rise to the polyanalytic version of the bicomplex Bergman spaces for which we provide the explicit expressions for their reproducing kernels.</p>

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Bicomplex Polyholomorphic Bergman Spaces Associated with a Bicomplex Magnetic Laplacian on the Discus

  • 期刊论文

  • 发表日期：

    2026年2月14日

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  • Issame Ahizoune,
  • Aiad Elgourari,
  • Allal Ghanmi

摘要

We consider a bicomplex analogue of the Landau Hamiltonian defined via its idempotent representation as a couple of the classical Landau Hamiltonians on two separate complex discs. We provide a complete characterization of its \(L^2\) L 2 -eigenspaces when acting on the so-called bicomplex p-Hilbert space, which next employed to explore the common eigenfunction problem associated with the magnetic bc-Laplacian and its \(\dagger \) † -conjugate. The corresponding eigenspaces give rise to the polyanalytic version of the bicomplex Bergman spaces for which we provide the explicit expressions for their reproducing kernels.