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PreprintarXiv licencearXiv

Algebras with Variable Operator-Valued Structural Constants and Their Applications

  • Vitalii Shpakivskyi
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Abstract

We introduce a new class of algebras with variable operator-valued structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the structural operators are established. It is shown that the components of monogenic functions satisfy second-order operator-differential equations with variable coefficients, and converse results are proved. The proposed approach provides a constructive method for obtaining solutions of various differential, integro-differential, and functional-differential equations. Several illustrative examples are presented.

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Cite

BibTeXRIS
BibTeX
@misc{shpakivskyi2026algebras,
  title = {{Algebras with Variable Operator-Valued Structural Constants and Their Applications}},
  author = {Vitalii Shpakivskyi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31628},
  eprint = {2609.31628},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31628},
}
RIS
TY  - UNPB
TI  - Algebras with Variable Operator-Valued Structural Constants and Their Applications
AU  - Vitalii Shpakivskyi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.31628
UR  - https://arxiv.org/abs/2609.31628
AB  - We introduce a new class of algebras with variable operator-valued structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the structural operators are established. It is shown that the components of monogenic functions satisfy second-order operator-differential equations with variable coefficients, and converse results are proved. The proposed approach provides a constructive method for obtaining solutions of various differential, integro-differential, and functional-differential equations. Several illustrative examples are presented.
ER  -