Cover Image

Constructive description of monogenic functions in a three-dimensional harmonic algebra with one-dimensional radical

We present a constructive description of monogenic functions that take values in a three-dimensional commutative harmonic algebra with one-dimensional radical by using analytic functions of complex variable. It is shown that monogenic functions have the Gâteaux derivatives of all orders.

Saved in:

Bibliographic Details
Date:	2013
Main Authors:	Plaksa, S. A., Pukhtaevich, R. P., Плакса, С. А., Пухтаевич, Р. П.
Format:	Article
Language:	Russian English
Published:	Institute of Mathematics, NAS of Ukraine 2013
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/2450
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Constructive description of monogenic functions in a three-dimensional harmonic algebra with one-dimensional radical
by: S. A. Plaksa, et al.
Published: (2013)

On the Logarithmic Residues of Monogenic functions in a Three-Dimensional Harmonic Algebra with Two-Dimensional Radical
by: Plaksa, S. A., et al.
Published: (2013)

On the Logarithmic Residues of Monogenic functions in a Three-Dimensional Harmonic Algebra with Two-Dimensional Radical
by: S. A. Plaksa, et al.
Published: (2013)

Constructive description of monogenic functions in a harmonic algebra of the third rank
by: Plaksa, S. A., et al.
Published: (2010)

The Cauchy type integral on the straight line in three-dimensional harmonic algebra with one-dimensional radical
by: R. P. Pukhtaievych, et al.
Published: (2015)

An analog of the Men’shov – Trokhimchuk theorem for monogenic functions in a three-dimensional commutative algebra
by: Tkachuk, M. V., et al.
Published: (2021)

Constructive description of monogenic functions in finite dimensional commutative algebras
by: V. S. Shpakivskyi
Published: (2015)

Monogenic functions in a three-dimensional harmonic semi-simple algebra
by: R. P. Pukhtaievych
Published: (2013)

On differentiable and monogenic functions in a harmonic algebra
by: S. A. Plaksa
Published: (2017)

Monogenic functions in a biharmonic algebra
by: Gryshchuk, S. V., et al.
Published: (2009)

An analog of the Men&#039;shov–Trokhimchuk theorem for monogenic functions in a three-dimensional commutative algebra
by: M. V. Tkachuk, et al.
Published: (2021)

Конструктивное описание моногенных функций в трехмерной гармонической алгебре с одномерным радикалом
by: Плакса, С.А., et al.
Published: (2013)

Monogenic functions in finite-dimensional commutative associative algebras
by: V. S. Shpakivskyi
Published: (2015)

Potential fields with axial symmetry and algebras of monogenic functions of vector variables. III
by: Mel'nichenko, I. P., et al.
Published: (1997)

Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. II
by: Mel'nichenko, I. P., et al.
Published: (1996)

Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I
by: Mel'nichenko, I. P., et al.
Published: (1996)

Potentials for solenoidal fields using the three-dimensional $\varphi$-harmonic cyclic algebra
by: Díaz-Marín, Homero G., et al.
Published: (2025)

Integral theorems for monogenic functions in an infinite-dimensional space with a commutative multiplication
by: S. A. Plaksa
Published: (2013)

Monogenic functions in two dimensional commutative algebras to equations of plane orthotropy
by: C. V. Hryshchuk
Published: (2018)

Biharmonic problem in an angle and monogenic functions
by: Gryshchuk, S. V., et al.
Published: (2026)

Three-dimensional Lie algebras for a one class of wave equations
by: O. V. Mahda
Published: (2017)

Algebras of Functionally Invariant Solutions of the Three-Dimensional Laplace Equation
by: Mel'nichenko, I. P., et al.
Published: (2003)

Monogenic functions in commutative algebras associated with classical equations of mathematical physics
by: S. A. Plaksa
Published: (2018)

To the construction of three-dimensional spiral-helix tubular solar collector
by: Мацевитый, Ю. М., et al.
Published: (2016)

To the construction of three-dimensional spiral-helix tubular solar collector
by: Мацевитый, Ю. М., et al.
Published: (2016)

Cohomogeneity One Dynamics on Three Dimensional Minkowski Space
by: P. Ahmadi
Published: (2019)

Monogenic functions in commutative algebras associated with classical equations of mathematical physics
by: Plaksa, S.A.
Published: (2018)

To the construction of three-dimensional spiral-helix tubular solar collector
by: Ju. M. Matsevityj, et al.
Published: (2011)

Finite-dimensional subalgebras in polynomial Lie algebras of rank one
by: Arzhantsev, I. V., et al.
Published: (2011)

Fermionic versus bosonic descriptions of one-dimensional spin-gapped antiferromagnets
by: Yamamoto, Shoji, et al.
Published: (2005)

Sound insulation properties of one-dimensional three-layered plate
by: L. A. Igumnov, et al.
Published: (2013)

lozynskyi one option of constructing three-dimensional distribution of the mass and its derivatives for a spherical planet earth
by: M. Fys, et al.
Published: (2016)

Constructing a two-dimensional mosaic by means of one pattern
by: A. G. Donets, et al.
Published: (2016)

Finite-dimensional subalgebras in polynomial Lie algebras of rank one
by: Arzhantsev, I.V., et al.
Published: (2011)

Hausdorff analytic functions in a three-dimensional associative noncommutative algebra
by: V. Shpakivskyi, et al.
Published: (2022)

Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
by: Korepanov, I.G.
Published: (2011)

Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler-Coulomb Potential
by: Tanoudis, Y., et al.
Published: (2011)

Discrete models on one-dimensional net with the preset Lie algebra of symmetries
by: Balinsky , A. I., et al.
Published: (1992)

Three-Dimensional Matrix Superpotentials
by: Karadzhov, Yu. A., et al.
Published: (2012)

Constructive description of classes of harmonic functions with peculiarities on the quasi-conformal arc
by: Andrievsky, V. V., et al.
Published: (1987)