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Abstract <p>The concept of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L\)</EquationSource> <!--LobJMat2560917Borovikov-m3--> </InlineEquation>-special domain appeared in the early 2000s. This analytical characteristic of domains in the complex plane is related to the problem on uniform approximation of functions on Carathéodory compacts in <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb{R}^{2}\)</EquationSource> <!--LobJMat2560917Borovikov-m4--> </InlineEquation> by polynomial solutions of homogeneous second-order elliptic partial differential equations <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(Lu=0\)</EquationSource> <!--LobJMat2560917Borovikov-m5--> </InlineEquation> with constant complex coefficients. In this paper, new properties and examples of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(L\)</EquationSource> <!--LobJMat2560917Borovikov-m6--> </InlineEquation>-special domains with algebraic boundaries are obtained.</p>

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On \(\boldsymbol{L}\)-Special Domains with Algebraic Boundaries

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • M. Borovikov

摘要

Abstract

The concept of \(L\) -special domain appeared in the early 2000s. This analytical characteristic of domains in the complex plane is related to the problem on uniform approximation of functions on Carathéodory compacts in \(\mathbb{R}^{2}\) by polynomial solutions of homogeneous second-order elliptic partial differential equations \(Lu=0\) with constant complex coefficients. In this paper, new properties and examples of \(L\) -special domains with algebraic boundaries are obtained.