Advances in Applied Clifford Algebras

, Volume 26, Issue 1, pp 417–434 | Cite as

Curvilinear Integral Theorems for Monogenic Functions in Commutative Associative Algebras

  • V. S. Shpakivskyi


We consider an arbitrary finite-dimensional commutative associative algebra, \({\mathbb{A}_n^m}\), with unit, over the field of complex number with m idempotents. Let e 1 = 1,e 2,e 3 be elements of \({\mathbb{A}_n^m}\) which are linearly independent over the field of real numbers. We consider monogenic (i.e. continuous and differentiable in the sense of Gateaux) functions of the variable xe 1 + ye 2 + ze 3, where x,y,z are real. For mentioned monogenic function we prove curvilinear analogues of the Cauchy integral theorem, the Morera theorem and the Cauchy integral formula.

Mathematics Subject Classification

Primary 30G35 Secondary 30G12 


Commutative associative algebra Cauchy integral theorem Morera theorem Cauchy integral formula 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Complex Analysis and Potential TheoryInstitute of Mathematics of the National Academy of Sciences of UkraineKiev 4Ukraine

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