Cauchy–Riemann Operators in Octonionic Analysis
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-018-0826-2
Abstract: In this paper we first recall the definition of the octonion algebra and its algebraic properties. We derive the so called $$e_4$$e4-calculus and using it we obtain the list of generalized Cauchy–Riemann systems for octonionic… read more here.
Keywords: riemann operators; cauchy riemann; operators octonionic; octonionic analysis ... See more keywords
A Cauchy problem for the Cauchy–Riemann operator
Sign Up to like & getrecommendations! Published in 2020 at "Afrika Matematika"
DOI: 10.1007/s13370-020-00810-4
Abstract: We study the Cauchy problem for a nonlinear elliptic equation with data on a piece $${\mathcal {S}}$$ S of the boundary surface $$\partial {\mathcal {X}}$$ ∂ X . By the Cauchy problem is meant any… read more here.
Keywords: cauchy riemann; cauchy problem; cauchy; riemann operator ... See more keywords
Riemann–Hilbert problem for the Cauchy–Riemann operator in lens and lune
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DOI: 10.1080/17476933.2016.1244189
Abstract: Abstract This article is devoted to study the solvability of the Riemann–Hilbert problem, with arbitrary index, for the Cauchy–Riemann operator in a lens and two complementary lunes. We generalize the corresponding results obtained by Begehr… read more here.
Keywords: riemann hilbert; cauchy riemann; hilbert problem; operator lens ... See more keywords
Riemann–Hilbert problems for null-solutions to iterated generalized Cauchy–Riemann equation on upper half ball
Sign Up to like & getrecommendations! Published in 2019 at "Complex Variables and Elliptic Equations"
DOI: 10.1080/17476933.2019.1664484
Abstract: Abstract We study Riemann–Hilbert boundary value problems with variable coefficients for axially symmetric null-solutions to the iterated generalized Cauchy–Riemann equation, defined over the upper half unit ball centred at the origin in four-dimensional Euclidean space.… read more here.
Keywords: null solutions; cauchy riemann; riemann equation; generalized cauchy ... See more keywords
Exact solutions for some classes of non-elliptic Cauchy–Riemann type systems with singular coefficients
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DOI: 10.1080/17476933.2024.2364645
Abstract: This paper deals with the solutions for some classes of non-elliptic Cauchy–Riemann type systems with singular coefficients.We give an explicit representation of the solutions and study their singularities read more here.
Keywords: solutions classes; non elliptic; riemann type; cauchy riemann ... See more keywords
Representation of the general solution of an equation of the Cauchy–Riemann type with a supersingular circle and a singular point
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DOI: 10.1134/s0012266117060118
Abstract: For a generalized system of the Cauchy–Riemann type with complex conjugation whose coefficients admit a strong singularity on a circle and a weak singularity at a point, we find an integral representation of the general… read more here.
Keywords: riemann type; general solution; cauchy riemann; representation general ... See more keywords
Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces
Sign Up to like & getrecommendations! Published in 2017 at "Siberian Mathematical Journal"
DOI: 10.1134/s0037446617010189
Abstract: We establish an analog of Hörmander’s Theorem on solvability of the inhomogeneous Cauchy–Riemann equation for a space of measurable functions satisfying a system of uniform estimates. The result is formulated in terms of the weight… read more here.
Keywords: riemann equation; cauchy riemann; solvability inhomogeneous; inhomogeneous cauchy ... See more keywords
On Continuation of Solutions of Generalized Cauchy–Riemann System in an Unbounded Subdomain of Multidimensional Space
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DOI: 10.3103/s1066369x21020031
Abstract: In this paper, we consider the problem of recovery of solutions to a generalized Cauchy–Riemann system in an unbounded subdomain of a multidimensional space from their values on a part of the domain boundary. With… read more here.
Keywords: unbounded subdomain; riemann system; cauchy riemann; system unbounded ... See more keywords
Scator Holomorphic Functions
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DOI: 10.3390/axioms14110798
Abstract: Scators form a linear space equipped with a specific non-distributive product. In the elliptic case they can be interpreted as a kind of hypercomplex number. The requirement that the scator partial derivatives are direction-independent leads… read more here.
Keywords: cauchy riemann; scator holomorphic; holomorphic functions;
Multi-Dimensional Analytic Functions for Laplace Equations and Generalized Cauchy–Riemann Equations
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DOI: 10.3390/math13081246
Abstract: A new concept of projective solution is introduced for the multi-dimensional Laplace equations. We project the field point onto a characteristic vector to obtain a projective variable, which can be used to reduce the Laplace… read more here.
Keywords: riemann equations; laplace equations; cauchy riemann; multi dimensional ... See more keywords