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Algebras with Variable Structural Constants and Their Applications

  • Vitalii Shpakivskyi
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Abstract

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

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Cite

BibTeXRIS
BibTeX
@misc{shpakivskyi2026algebras,
  title = {{Algebras with Variable Structural Constants and Their Applications}},
  author = {Vitalii Shpakivskyi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.31627},
  eprint = {2609.31627},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.31627},
}
RIS
TY  - UNPB
TI  - Algebras with Variable Structural Constants and Their Applications
AU  - Vitalii Shpakivskyi
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.31627
UR  - https://arxiv.org/abs/2609.31627
AB  - We introduce a new class of algebras with variable structural constants and develop elements of the theory of monogenic functions in such algebras. Compatibility conditions for the structural functions are established. It is shown that the components of monogenic functions satisfy certain second-order partial differential equations with variable coefficients, and converse results are proved. This approach provides a constructive method for obtaining explicit solutions of such equations. Several illustrative examples are presented.
ER  -