Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 31 min ago
PreprintarXiv licencearXiv

Covariance property for a quaternionic fractional Cauchy-Riemann operator under affine transformation

  • Isidro Paulino-Basurto
  • José Oscar Gonzáles-Cervantes
  • Juan Bory-Reyes
  • Hung Manh Nguyen
Open at sourcePDFDOICite

Abstract

In this paper, we continue the development of the foundations of a quaternionic function theory that is associated to a fractional proportional Cauchy-Riemann type operator acting on quaternionic functions. We introduce a new class of fractional hyperholomorphic functions adapted to affine transformations of the domain, and study the corresponding quaternionic right module structure. In particular, we establish versions of the Stokes, Borel-Pompeiu and Cauchy formulas for this function theory. A covariance property of the fractional operator under affine transformations is proved, showing that the composition with an affine map, weighted by a suitable quaternionic factor, preserves the class of fractional hyperholomorphic functions. The result is shown to include the case considered previously by the authors, and extends their covariance property to the setting of affine transformations.

Related

  1. Quaternionic Elasticity Theory with Local Fractional Derivatives
    Hung Manh Nguyen, Juan Bory-Reyes
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. A note on the Browder S-spectrum of a bounded quaternionic operator
    Mohamed Ali Dbeibia
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. A Law of Fractional Logarithm for Nested Complex Sample Covariance Matrices
    Xiufan Yang
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Independently Verified Causal Spatio-Temporal Covariance Under Correlated Amplitude and Pointing Noise in Fractional Nonlocal Photo-Thermoelastic Semiconductors
    Adel Emam, S. M. Khaled, A. El-Dali +1
    Fractal and FractionalPeer-reviewedCC BY 4.0Analysis & PDEsCrossref
  5. The UMD property of symmetric operator spaces
    J Huang, F Sukochev
    HALPreprintPublisher termsFull textAnalysis & PDEsHALarXiv

Cite

BibTeXRIS
BibTeX
@misc{paulinobasurto2026covariance,
  title = {{Covariance property for a quaternionic fractional Cauchy-Riemann operator under affine transformation}},
  author = {Isidro Paulino-Basurto and José Oscar Gonzáles-Cervantes and Juan Bory-Reyes and Hung Manh Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08744},
  eprint = {2609.08744},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08744},
}
RIS
TY  - UNPB
TI  - Covariance property for a quaternionic fractional Cauchy-Riemann operator under affine transformation
AU  - Isidro Paulino-Basurto
AU  - José Oscar Gonzáles-Cervantes
AU  - Juan Bory-Reyes
AU  - Hung Manh Nguyen
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08744
UR  - https://arxiv.org/abs/2609.08744
AB  - In this paper, we continue the development of the foundations of a quaternionic function theory that is associated to a fractional proportional Cauchy-Riemann type operator acting on quaternionic functions. We introduce a new class of fractional hyperholomorphic functions adapted to affine transformations of the domain, and study the corresponding quaternionic right module structure. In particular, we establish versions of the Stokes, Borel-Pompeiu and Cauchy formulas for this function theory. A covariance property of the fractional operator under affine transformations is proved, showing that the composition with an affine map, weighted by a suitable quaternionic factor, preserves the class of fractional hyperholomorphic functions. The result is shown to include the case considered previously by the authors, and extends their covariance property to the setting of affine transformations.
ER  -