ON INVARIANCE OF THE GENERALIZED CAUCHY-RIEMANN EQUATIONS
Abstract
The С1 class of mappings domains in R2 , satisfying the system of generalized Cauchy-Riemann equations is considered. Sufficient conditions for the closure of this class relative to the operations of addition, superposition and reverse mapping were found. The second part of the paper introduces the found conditions for which there are maps that satisfy the generalized Cauchy-Riemann system with a given coefficient matrix of the system.
About the Authors
N. A. Shvemler
Tyumen State University
Russian Federation
Natalia A. Shvemler – post-graduate student at the Department of Mathematical Analysis and Functions Theory, Institute of Mathematics and Computer Sciences
Russian Federation
Natalia A. Shvemler – post-graduate student at the Department of Mathematical Analysis and Functions Theory, Institute of Mathematics and Computer Sciences
T. G. Latfullin
Tyumen State University
Russian Federation
Tagir G. Latfullin – Doctor of Physics and Mathematics, Professor at the Department of Mathematical Analysis and Functions Theory, Institute of Mathematics and Computer Sciences
Russian Federation
Tagir G. Latfullin – Doctor of Physics and Mathematics, Professor at the Department of Mathematical Analysis and Functions Theory, Institute of Mathematics and Computer Sciences
References
1. Векуа И. Н. Об одном свойстве решений обобщенной системы уравнений Коши-Римана // Сообщ. АН ГССР. 1953. Т. 14. № 8. С. 449 – 453.
2. Латфуллин Т. Г. Квазикомфорные отображения, удовлетворяющие условиям, подобным условиям КошиРимана // Труды Международной конференции Ломоносовские чтения на Алтае. 2014. С. 323 – 327.
3. Латфуллин Т. Г. Когда однородная система УЧП первого порядка имеет линейное решение // Сб. науч. ст. Международной конференции «Ломоносовские чтения на Алтае». 2012. С. 314 – 318.
4. Морев И. А. Об одном обобщении уравнений Коши-Римана и гармоничности моногенных гиперкомплексных функций // Известия вузов. Математика. 1958. № 3. С. 176 – 182.
5. Ward J. A. From Generalized Cauchy-Riemann Equations to Linear Algebras Proceedings of the American Mathematical Society. Vol. 4. № 3. (Jun., 1953). P. 456 – 461.
6. Williams K. P. A Generalization of the Cauchy-Riemann Equations. The Annals of Mathematics, 2nd Ser. Vol. 30. № 1/4. (1928 – 1929). P. 206 – 210.
Review
For citations:
Shvemler N.A., Latfullin T.G. ON INVARIANCE OF THE GENERALIZED CAUCHY-RIEMANN EQUATIONS. SibScript. 2015;(4-3):140-145. (In Russ.)
Views:
360
Email this article 