Scholarlink

<p>We prove the existence of approximate solutions in the regular Denjoy–Carleman sense for some systems of smooth pairwise commuting complex vector fields. Such approximate solutions provide a well-defined notion of Denjoy–Carleman wave front set of distributions on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10144_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {C}^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="script">C</mi> </mrow> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation>-smooth maximally real submanifolds in complex space which can be characterized in terms of the decay of a Fourier–Bros–Iagolnitzer transform. We also apply the approximate solutions to analyze the Denjoy–Carleman microlocal regularity of solutions of certain systems of first-order nonlinear partial differential equations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Denjoy–Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Spaces

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月12日

查看全文
  • Nicholas Braun Rodrigues,
  • Antonio Victor da Silva Jr.

摘要

We prove the existence of approximate solutions in the regular Denjoy–Carleman sense for some systems of smooth pairwise commuting complex vector fields. Such approximate solutions provide a well-defined notion of Denjoy–Carleman wave front set of distributions on \(\mathcal {C}^\infty \) C ∞ -smooth maximally real submanifolds in complex space which can be characterized in terms of the decay of a Fourier–Bros–Iagolnitzer transform. We also apply the approximate solutions to analyze the Denjoy–Carleman microlocal regularity of solutions of certain systems of first-order nonlinear partial differential equations.