Cauchy theorem for a surface integral in commutative algebras

DOI10.1080/17476933.2013.845178zbMath1297.30074arXiv1305.4500OpenAlexW2063129858MaRDI QIDQ3189372

Sergiy A. Plaksa, Vitalii S. Shpakivskyi

Publication date: 9 September 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.4500

zbMATH Keywords

harmonic functionLaplace equationmonogenic functionCauchy integral theoremhyperholomorphic functionCauchy-Riemann conditionsharmonic commutative Banach algebracommutative associative Banach algebra

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Vector-valued set functions, measures and integrals (28B05)

Related Items (7)

σ-monogenic functions in commutative algebras ⋮ Monogenic functions and harmonic vectors ⋮ On an attempt to introduce a notion of bounded index for the Fueter regular functions of the quaternionic variable ⋮ Conformable fractional derivative in commutative algebras ⋮ On the Cauchy theorem for hyperholomorphic functions of spatial variable ⋮ Monogenic functions in commutative algebras associated with classical equations of mathematical physics ⋮ An extension of monogenic functions and spatial potentials

Cites Work

• Eigenvalue problems in the framework of Clifford analysis
• On hyperholomorphic functions of the space variable
• Slice monogenic functions
• The Gauss-Green theorem for fractal boundaries
• Boundary value problems for quaternionic monogenic functions on non-smooth surfaces
• Minkowski dimension and Cauchy transform in Clifford analysis
• Clifford Cauchy type integrals on Ahlfors-David regular surfaces in \(\mathbb R^{m+1}\)
• Factorization of the nonlinear Schrödinger equation and applications
• Quaternionic analysis
• Surface integrals for domains with fractal boundaries and some applications to elasticity

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