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

Abstract

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.

Authors:
; ;  [1]
  1. Al-Farabi Kazakh National University (Kazakhstan)
Publication Date:
OSTI Identifier:
22771553
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 229; Journal 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); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CAUCHY PROBLEM; FOUR-DIMENSIONAL CALCULATIONS; HARMONICS; MANY-DIMENSIONAL CALCULATIONS; MATHEMATICAL SOLUTIONS; RIEMANN FUNCTION

Citation Formats

Tokibetov, J. A., Abduakhitova, G. E., and Sarsekeeva, A. S. Multidimensional Analogs of the Cauchy–Riemann System and Representations of Their Solutions via Harmonic Functions. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3671-X.
Tokibetov, J. A., Abduakhitova, G. E., & Sarsekeeva, A. S. Multidimensional Analogs of the Cauchy–Riemann System and Representations of Their Solutions via Harmonic Functions. United States. doi:10.1007/S10958-018-3671-X.
Tokibetov, J. A., Abduakhitova, G. E., and Sarsekeeva, A. S. Thu . "Multidimensional Analogs of the Cauchy–Riemann System and Representations of Their Solutions via Harmonic Functions". United States. doi:10.1007/S10958-018-3671-X.
@article{osti_22771553,
title = {Multidimensional Analogs of the Cauchy–Riemann System and Representations of Their Solutions via Harmonic Functions},
author = {Tokibetov, J. A. and Abduakhitova, G. E. and Sarsekeeva, A. S.},
abstractNote = {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.},
doi = {10.1007/S10958-018-3671-X},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 2,
volume = 229,
place = {United States},
year = {2018},
month = {2}
}