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<p>We study the linear topological invariant <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete characterization of the property <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((\Omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for such spaces in terms of an explicit condition on the defining weight function systems. As an application, we investigate the surjectivity of the Cauchy-Riemann operator on certain weighted spaces of vector-valued smooth functions.</p>

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A linear topological invariant for weighted spaces of holomorphic functions

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Andreas Debrouwere,
  • Quinten Van Boxstael

摘要

We study the linear topological invariant \((\Omega )\) ( Ω ) for a class of Fréchet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete characterization of the property \((\Omega )\) ( Ω ) for such spaces in terms of an explicit condition on the defining weight function systems. As an application, we investigate the surjectivity of the Cauchy-Riemann operator on certain weighted spaces of vector-valued smooth functions.