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<p>In this paper, we characterise Hölder continuity, two-microlocal spaces, and the Sobolev wavefront set, and propose a novel representation of the solutions of Schrödinger equations for a free particle using the wavelet transform introduced by Moritoh in Moritoh (Tohoku Math J 47:555–565, 1995). Additionally, we discuss its application in determining the microlocally regular solutions to the Schrödinger equations of a free particle, providing a refined understanding of their microlocal regularity properties.</p>

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Characterisation of Two-Microlocal Spaces and Wavefront Sets by Wavelet Transforms and Their Application to Solutions of Schrödinger Equations

  • 期刊论文

  • 发表日期：

    2025年10月21日

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  • Ashish Pathak,
  • Anurag Mishra

摘要

In this paper, we characterise Hölder continuity, two-microlocal spaces, and the Sobolev wavefront set, and propose a novel representation of the solutions of Schrödinger equations for a free particle using the wavelet transform introduced by Moritoh in Moritoh (Tohoku Math J 47:555–565, 1995). Additionally, we discuss its application in determining the microlocally regular solutions to the Schrödinger equations of a free particle, providing a refined understanding of their microlocal regularity properties.