Cover Image

On hyperholomorphic functions of the space variable

For quaternionic-differentiable functions of a spatial variable, we prove a theorem on an integral over a closed surface. This theorem is an analog of the Cauchy theorem from complex analysis.

Saved in:

Bibliographic Details
Date:	2011
Main Authors:	Gerus, O. F., Герус, О. Ф.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 2011
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/2731
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

On the Cauchy theorem for hyperholomorphic functions of spatial variable
by: Herus, O.F.
Published: (2017)

On the Cauchy theorem for hyperholomorphic functions of spatial variable
by: O. F. Herus
Published: (2017)

Estimates for the modulus of a Cauchy-type integral and its derivatives
by: Gerus, O. F., et al.
Published: (1999)

Estimate of the modulus of continuity of a cauchy-type integral in a domain and on its boundary
by: Gerus, O. F., et al.
Published: (1996)

On the modulus of continuity of solid derivatives of a Cauchy-type integral
by: Gerus, O. F., et al.
Published: (1998)

Approximation of periodic functions of many variables by functions of smaller number of variables in Orlicz metric spaces
by: Babich, Yu. A., et al.
Published: (2018)

An estimate for the modulus of continuity of a quaternion singular Cauchy integral
by: Gerus, O. F., et al.
Published: (2010)

Approximation of periodic functions of many variables by functions of smaller number of variables in Orlicz metric spaces
by: Ju. A. Babich, et al.
Published: (2018)

Isometry of functional spaces with different number of variables
by: Bushev, D. M., et al.
Published: (1998)

Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions
by: T. A. Agoshkova
Published: (2013)

Approximation of Periodic Functions of Many Variables in Metric Spaces by Piecewise-Constant Functions
by: Agoshkova, T. A., et al.
Published: (2013)

Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent
by: Akgün, R., et al.
Published: (2011)

Best M-term trigonometric approximations of the classes of periodic functions of many variables in the space Lq
by: Konohrai, A. F., et al.
Published: (2008)

Elements of a non-gaussian analysis on the spaces of functions of infinitely many variables
by: Kachanovskii, N. A., et al.
Published: (2010)

Isometry of the functional spaces with different number of variables and some its applications in the theory of approximation of functions
by: D. N. Bushev
Published: (2019)

On a class of entire functions of many variables
by: Geche, F. I., et al.
Published: (1966)

Elements of a non-Gaussian analysis on the spaces of functions of infinitely many variables
by: Kachanovsky, N.A.
Published: (2010)

Approximation of the Classes HpΩ of Periodic Functions of Many Variables in the Space Lp
by: N. V. Derevianko
Published: (2014)

Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature
by: Ragnisco, O., et al.
Published: (2007)

Hermite interpolation polynomial for many-variable functions
by: O. F. Kashpur
Published: (2022)

Kolmogorov widths of the Nikol’skii – Besov classes of periodic functions of many variables in the space of quasi-continuous functions
by: Romanyuk , A. S., et al.
Published: (2022)

Linear widths of the classes $B^{\Omega}_{p, \theta}$ of periodic functions of many variables in the space $L_q$
by: Fedunyk, O. V., et al.
Published: (2006)

Approximation of the Classes $H_p^{Ω}$ of Periodic Functions of Many Variables in the Space $L_p$
by: Derev’yanko, N. V., et al.
Published: (2014)

Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces
by: Maslyuchenko, V. K., et al.
Published: (2000)

Orthoprojective widths of classes BΩ(ρ,θ) of periodis functions of variables in the space Lq
by: N. V. Derevianko
Published: (2013)

On total moduli of continuity for 2periodic functions of two variables in the space L_(2,2)
by: S. B. Vakarchuk, et al.
Published: (2017)

On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces
by: S. B. Vakarchuk, et al.
Published: (2014)

On the Best Polynomial Approximations of Entire Transcendental Functions of Many Complex Variables in Some Banach Spaces
by: Vakarchuk, S. B., et al.
Published: (2014)

Kolmogorov widths of the Nikol&#039;skii–Besov classes of periodic functions of many variables in the space of quasicontinuous functions
by: A. S. Romaniuk, et al.
Published: (2022)

Optimization of approximate integration of monotone functions of two variables
by: Babenko, V. F., et al.
Published: (1999)

Monogenic functions of double variable
by: V. S. Shpakivskyi, et al.
Published: (2013)

One inequality of the Landau – Kolmogorov type for periodic functions of two variable
by: Babenko, V. F., et al.
Published: (2019)

Approximations of classes $B^{Ω}_{p,θ}$ of functions of many variables by entire functions in the space $L_q (R^d)$
by: Yanchenko, S. Ya., et al.
Published: (2010)

Approximation of classes of periodic functions in one and many variables from the Nikol’skii – Besov and Sobolev spaces
by: Romanyuk, A. S., et al.
Published: (2022)

Estimations of linear widths of the classes HΩp periodic functions of many variables in the space Lq
by: N. V. Derevianko
Published: (2014)

Trigonometric widths of the classes $B_{p,θ}^ r$ of functions of many variables in the space $L_q$
by: Romanyuk, A. S., et al.
Published: (1998)

On Kolmogorov-type inequalities for fractional derivatives of functions of two variables
by: Babenko, V. F., et al.
Published: (2008)

Approximation of some classes of functions of many variables by harmonic splines
by: Babenko, V. F., et al.
Published: (2012)

Asymptotic behavior of Lebesgue functions of two variables
by: Kuznetsovci, O. I., et al.
Published: (1995)

On total moduli of continuity for $2\pi$-periodic functions of two variables in the space $L_{2,2}$
by: Vakarchuk, M. B., et al.
Published: (2017)