A boundary Morera theorem

We consider a class of so-called quaternionic G-monogenic mappings associatedwith m-dimensional (m 2 f2; 3; 4g) partial differential equations and propose a description of allmappings from this class by using four analytic functions of complex variable. For G-monogenicmappings we generalize some analogues of classical integral theorems of the holomorphic functiontheory of the complex variable (the surface and the curvilinear Cauchy integral theorems,the Cauchy integral formula, the Morera theorem), and Taylor’s and Laurent’s expansions.Moreover, we investigated the relation between G-monogenic and H-monogenic (differentiablein the sense of Hausdorff) quaternionic mappings.

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Boundary Version of the Morera Theorem for a Matrix Ball of the Second Type

Journal of Siberian Federal University Mathematics & Physics ◽

10.17516/1997-1397-2014-7-4-466-471 ◽

2014 ◽

Vol 7 (4) ◽

pp. 466-471

Author(s):

Gulmirza Kh. Khudayberganov ◽

◽

Zokirbek K. Matyakubov ◽

Keyword(s):

Morera Theorem ◽

Boundary Version

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Morera Theorem

Van Nostrand's Scientific Encyclopedia ◽

10.1002/0471743984.vse4993 ◽

2005 ◽

Keyword(s):

Morera Theorem

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A generalization of the multidimensional Morera theorem

Ukrainian Mathematical Journal ◽

10.1007/bf01089304 ◽

1979 ◽

Vol 30 (3) ◽

pp. 265-269

Author(s):

A. V. Bondar'

Keyword(s):

Morera Theorem

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Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/auom-2014-0018 ◽

2014 ◽

Vol 22 (1) ◽

pp. 221-235 ◽

Cited By ~ 4

Author(s):

S. A. Plaksa ◽

R. P. Pukhtaievych

Keyword(s):

Commutative Algebra ◽

Function Theory ◽

Integral Formula ◽

Monogenic Functions ◽

Cauchy Integral ◽

Constructive Description ◽

Finite Dimensional ◽

Morera Theorem ◽

Classical Integral ◽

Derivatives Of

AbstractWe 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.

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