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Abstract <p>We consider a multi-element linear equation for functions that are analytic in a plane with a cut along a segment of the imaginary axis and vanish at infinity. The solution is sought in the form of a Cauchy-type integral over this segment with an unknown density. The regularization of the obtained functional equation is carried out and the condition for its equivalence is found. The results are applied to the study of the Stieltjes moment problem with an exponential weight for entire functions of a known class A. The Borel transformation is used in this process.</p>

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Multi-Element Equations for Functions, Analytic in a Plane with a Cut along a Segment of the Imaginary Axis, and Their Applications

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • F. N. Garifyanov

摘要

Abstract

We consider a multi-element linear equation for functions that are analytic in a plane with a cut along a segment of the imaginary axis and vanish at infinity. The solution is sought in the form of a Cauchy-type integral over this segment with an unknown density. The regularization of the obtained functional equation is carried out and the condition for its equivalence is found. The results are applied to the study of the Stieltjes moment problem with an exponential weight for entire functions of a known class A. The Borel transformation is used in this process.