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Abstract <p>The theory of Noether operators in linear spaces without a norm and without topology is constructed. The correspondence between the elements of spaces established by the Noether operator is investigated. The necessary and sufficient conditions for the Noetherness of the linear operator are obtained. The properties of characteristic Noether operators and methods of their regularization are considered.</p>

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Algebraic Variant of Noether Operator Theory

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • N. B. Pleshchinskii

摘要

Abstract

The theory of Noether operators in linear spaces without a norm and without topology is constructed. The correspondence between the elements of spaces established by the Noether operator is investigated. The necessary and sufficient conditions for the Noetherness of the linear operator are obtained. The properties of characteristic Noether operators and methods of their regularization are considered.