Multidimensional Analogs of the Cauchy–Riemann System and Representations of Their Solutions via Harmonic Functions

Journal Article · Thu Feb 15 00:00:00 EST 2018 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/S10958-018-3671-X· OSTI ID:22771553

Tokibetov, J. A.; Abduakhitova, G. E.; Sarsekeeva, A. S. ^[1]

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1. Al-Farabi Kazakh National University (Kazakhstan)

At present, there are numerous multidimensional generalizations of holomorphic vectors. The most general of these is the four-dimensional generalization of the Cauchy–Riemann system. In the present work, by introducing two quaternion functions and the notion of quaternion differentiation, we obtain, for the first time, a five-dimensional generalization of holomorphic vectors. By using the representation of holomorphic vectors via the quaternion harmonic function and its derivatives, we consider the Riemann–Hilbert problem and one problem in a layer. A new solution of the Riemann–Hilbert problem in the five-dimensional half space is obtained.

• OSTI ID: 22771553
• Journal Information: Journal of Mathematical Sciences, Vol. 229, Issue 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 1072-3374
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CAUCHY PROBLEM
FOUR-DIMENSIONAL CALCULATIONS
HARMONICS
MANY-DIMENSIONAL CALCULATIONS
MATHEMATICAL SOLUTIONS
RIEMANN FUNCTION