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<p>The Strichartz inequality for solutions of free Schrödinger equation associated with the Dunkl Hermite operator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H_\kappa\)</EquationSource> </InlineEquation> is generalized to systems of orthonormal functions with initial data. Furthermore, a relation between the kernels of Schrödinger propagators <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(e^{-it H_\kappa }\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(e^{it\Delta _\kappa }\)</EquationSource> </InlineEquation> corresponding to the Dunkl Hermite and Dunkl Laplacian operators, is established. Using this relation, we establish the corresponding Strichartz inequality for solutions of the free Schrödinger equation associated with the Dunkl Laplacian, with initial data given by systems of orthonormal functions.</p>

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Strichartz inequality for orthonormal functions associated with Dunkl Laplacian and Hermite–Schrödinger operators

  • 期刊论文

  • 发表日期：

    2025年11月15日

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  • P. Jitendra Kumar Senapati,
  • Pradeep Boggarapu

摘要

The Strichartz inequality for solutions of free Schrödinger equation associated with the Dunkl Hermite operator \(H_\kappa\) is generalized to systems of orthonormal functions with initial data. Furthermore, a relation between the kernels of Schrödinger propagators \(e^{-it H_\kappa }\) and \(e^{it\Delta _\kappa }\) corresponding to the Dunkl Hermite and Dunkl Laplacian operators, is established. Using this relation, we establish the corresponding Strichartz inequality for solutions of the free Schrödinger equation associated with the Dunkl Laplacian, with initial data given by systems of orthonormal functions.