Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra
We obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic funct...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2014-12-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2014-0018 |
| _version_ | 1811272385232371712 |
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| author | Plaksa S. A. Pukhtaievych R. P. |
| author_facet | Plaksa S. A. Pukhtaievych R. P. |
| author_sort | Plaksa S. A. |
| collection | DOAJ |
| description | We obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic functions we prove also analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, the Morera theorem and the Cauchy integral formula. |
| first_indexed | 2024-04-12T22:39:22Z |
| format | Article |
| id | doaj.art-73cb05392a10469ba418753a159d3c15 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-12T22:39:22Z |
| publishDate | 2014-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-73cb05392a10469ba418753a159d3c152022-12-22T03:13:47ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352014-12-0122122123510.2478/auom-2014-0018Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative AlgebraPlaksa S. A.0Pukhtaievych R. P.1Department of complex analysis and potential theory, Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, Kiev, UkraineDepartment of complex analysis and potential theory, Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereshchenkivska Street, Kiev, UkraineWe obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic functions we prove also analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, the Morera theorem and the Cauchy integral formula.https://doi.org/10.2478/auom-2014-0018commutative banach algebramonogenic functionlaplace equationcauchy integral theoremcauchy integral formulamorera theorem |
| spellingShingle | Plaksa S. A. Pukhtaievych R. P. Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica commutative banach algebra monogenic function laplace equation cauchy integral theorem cauchy integral formula morera theorem |
| title | Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra |
| title_full | Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra |
| title_fullStr | Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra |
| title_full_unstemmed | Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra |
| title_short | Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra |
| title_sort | monogenic functions in a finite dimensional semi simple commutative algebra |
| topic | commutative banach algebra monogenic function laplace equation cauchy integral theorem cauchy integral formula morera theorem |
| url | https://doi.org/10.2478/auom-2014-0018 |
| work_keys_str_mv | AT plaksasa monogenicfunctionsinafinitedimensionalsemisimplecommutativealgebra AT pukhtaievychrp monogenicfunctionsinafinitedimensionalsemisimplecommutativealgebra |