Skip to content
DraconiticResearch
Search Sources API
194,226 studies31 sourcesUpdated 18 min ago
PreprintarXiv licencearXiv

Operator Algebras and Their Applications

  • Vitalii Shpakivskyi
Open at sourcePDFDOICite

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.

Related

  1. Algebras with Variable Operator-Valued Structural Constants and Their Applications
    Vitalii Shpakivskyi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv
  2. Associativity of operator convolutions for group actions on von Neumann algebras
    Hannes Wendt
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Classification of Strongly Rational Vertex Operator Algebras with Central and Effective Central Charge One
    Shun Xu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. The Ulam--Kaplansky problem in operator algebras
    Chunlan Jiang, Minghui Ma, Rui Shi +1
    arXivPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsarXiv
  5. Reverse Module Categories of Vertex Operator Algebras
    Chongying Dong, Binghui Li, Li Ren +1
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{shpakivskyi2026operator,
  title = {{Operator Algebras and Their Applications}},
  author = {Vitalii Shpakivskyi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12478},
  eprint = {2610.12478},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12478},
}
RIS
TY  - UNPB
TI  - Operator Algebras and Their Applications
AU  - Vitalii Shpakivskyi
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.12478
UR  - https://arxiv.org/abs/2610.12478
AB  - 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.
ER  -