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arXiv · 2610.12478

Operator Algebras and Their Applications

Vitalii Shpakivskyi
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Abstract

We introduce a new class of commutative associative algebras whose structural constants are linear operators acting in a linear topological space. An analogue of the theory of monogenic functions is developed for such algebras. It is shown that the components of monogenic functions satisfy second-order operator-differential equations. This approach provides a constructive method for obtaining solutions of various partial differential and integro-differential equations. Several illustrative examples are presented.

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BibTeXRIS

Vitalii Shpakivskyi. 2026-08-28. Operator Algebras and Their Applications. https://arxiv.org/abs/2610.12478

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