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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…
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Keywords:
riemann operators;
cauchy riemann;
operators octonionic;
octonionic analysis ... See more keywords
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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…
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Keywords:
cauchy riemann;
cauchy problem;
cauchy;
riemann operator ... See more keywords
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Published in 2017 at "Complex Variables and Elliptic Equations"
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…
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Keywords:
riemann hilbert;
cauchy riemann;
hilbert problem;
operator lens ... See more keywords
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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.…
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Keywords:
null solutions;
cauchy riemann;
riemann equation;
generalized cauchy ... See more keywords
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Published in 2017 at "Differential Equations"
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…
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Keywords:
riemann type;
general solution;
cauchy riemann;
representation general ... See more keywords
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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…
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Keywords:
riemann equation;
cauchy riemann;
solvability inhomogeneous;
inhomogeneous cauchy ... See more keywords
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Published in 2021 at "Russian Mathematics"
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…
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Keywords:
unbounded subdomain;
riemann system;
cauchy riemann;
system unbounded ... See more keywords