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Abstract <p>A summation method for Fourier series associated with a generalized mixed problem for the telegraph equation in a semi-infinite strip is proposed. The concept of the regularity of a summation method is introduced. It is shown that the generalized sum produced by this method can be used as a solution of the generalized mixed problem. Here, the generalized sum is specified by an exponentially converging function series. In the case of smooth initial data, this series gives a strong solution of the original pro-blem.</p>

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Summation Method for Fourier Series Associated with a Mixed Problem for the Inhomogeneous Telegraph Equation

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • I. S. Lomov

摘要

Abstract

A summation method for Fourier series associated with a generalized mixed problem for the telegraph equation in a semi-infinite strip is proposed. The concept of the regularity of a summation method is introduced. It is shown that the generalized sum produced by this method can be used as a solution of the generalized mixed problem. Here, the generalized sum is specified by an exponentially converging function series. In the case of smooth initial data, this series gives a strong solution of the original pro-blem.