Singular Generalized Analytic Functions

2019 ◽  
Vol 237 (1) ◽  
pp. 30-109
Author(s):  
G. Giorgadze ◽  
V. Jikia ◽  
G. Makatsaria
Keyword(s):  
Analytic Functions ◽  
Generalized Analytic Functions

Logarithmic Potential and Generalized Analytic Functions

2021 ◽  
Author(s):  
V. Gutlyanskiĭ ◽  
O. Nesmelova ◽  
V. Ryazanov ◽  
A. Yefimushkin
Keyword(s):  
Analytic Functions ◽  
Logarithmic Potential ◽  
Generalized Analytic Functions

GENERALIZED ANALYTIC FUNCTIONS OF SEVERAL VARIABLES

1979 ◽  
Vol 35 (2) ◽  
pp. 181-205 ◽  
Author(s):  
G A Magomedov ◽  
V P Palamodov
Keyword(s):  
Analytic Functions ◽  
Generalized Analytic Functions ◽  
Several Variables

scholarly journals Generalized Analytic Functions in Higher Dimensions

2007 ◽  
Vol 14 (3) ◽  
pp. 581-595
Author(s):  
Wolfgang Tutschke
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Analytic Functions ◽  
Boundary Value ◽  
Higher Dimensions ◽  
Partial Differential ◽  
Generalized Analytic Functions ◽  
Linear Partial Differential Equations ◽  
Weakly Singular

Abstract Originally I. N. Vekua's theory of generalized analytic functions dealt only with linear systems of partial differential equations in the plane. The present paper shows why I. N. Vekua's ideas are also fruitful for the solution of linear and non-linear partial differential equations in higher dimensions. One of the highlights of the theory of generalized analytic functions in the plane is the reduction of boundary value problems for general (linear or nonlinear) equations to boundary value problems for holomorphic functions using the well-known weakly singular and strongly singular 𝑇- and П-operators, respectively. The present paper is mainly aimed at reducing boundary value problems in higher dimensions to boundary value problems for monogenic functions.

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