[图书][B] Classical complex analysis

M Gonzalez - 1991 - books.google.com
Text on the theory of functions of one complex variable contains, with many elaborations, the
subject of the courses and seminars offered by the author over a period of 40 years, and …

When is a function that satisfies the Cauchy-Riemann equations analytic?

JD Gray, SA Morris - The American Mathematical Monthly, 1978 - Taylor & Francis
THEOREM 1. Iff= u+ iv, defined on a domain D, is such that (i) au I ax, au I ay, av I ax, av I ay
exist everywhere in D,(ii) u, v satisfy the Cauchy-Riemann equations everywhere in D, and if …

[图书][B] A complex analysis problem book

D Alpay - 2011 - Springer
Such functions bear various names: They are said to be holomorphic in Ω, or analytic in Ω;
the terms C-differentiable, differentiable and regular are also used. A key result in the theory …

The regularity of inverses to Sobolev mappings and the theory of-homeomorphisms

SK Vodopyanov - Siberian Mathematical Journal, 2020 - Springer
We prove that each homeomorphism φ:D→D^′ of Euclidean domains in 𝕉^n, n≧2,
belonging to the Sobolev class W^1_p,loc(D), where p∈1,∞), and having finite distortion …

Basic properties of monogenic functions in a biharmonic plane

SV Gryshchuk, SA Plaksa - Complex analysis and dynamical …, 2013 - books.google.com
We consider monogenic functions given in a biharmonic plane and taking values in a
commutative algebra associated with the biharmonic equation. For the mentioned functions …

Monogenic functions in commutative algebras associated with classical equations of mathematical physics

SA Plaksa - Journal of Mathematical Sciences, 2019 - Springer
The methods involving the functions analytic in a complex plane for plane potential fields
inspire the search for the analogous efficient methods for solving the spatial and …

The removability problem for functions with zero spherical means

VV Volchkov, NP Volchkova - Siberian Mathematical Journal, 2017 - Springer
THE REMOVABILITY PROBLEM FOR FUNCTIONS WITH ZERO SPHERICAL MEANS Page 1
Siberian Mathematical Journal, Vol. 58, No. 3, pp. 419–426, 2017 Original Russian Text …

Integral Theorems and Series in the Three-Dimensional Harmonic Algebra with Two-Dimensional Radical

SA Plaksa, VS Shpakivskyi - Monogenic Functions in Spaces with …, 2023 - Springer
In this chapter, for monogenic functions taking values in the three-dimensional harmonic
algebra with two-dimensional radical, we establish basic properties analogous to properties …

On the theory of degenerate alternating beltrami equations

AN Kondrashov - Siberian mathematical journal, 2012 - Springer
ON THE THEORY OF DEGENERATE ALTERNATING BELTRAMI EQUATIONS Page 1 Siberian
Mathematical Journal, Vol. 53, No. 6, pp. 1061–1074, 2012 Original Russian Text Copyright c …

Sufficient conditions for the finite-valence of analytic functions and their applications

FG Avkhadiev, LA Aksent'ev, AM Elizarov - Journal of Soviet Mathematics, 1990 - Springer
In the first part of the paper there is given a survey of the contemporary state of the theory of
the sufficient univalence and p-valence conditions for analytic and meromorphic functions of …